I use portaudio in a Cpp work.
My signal model treats the only 16000Hz audio input and
When the First released my work, I don't need to use 44100 sample rate. It was just about 48000Hz microphone.
So I resampled my signal like 48000 -> 16000 -> 48000 with a simple decimation algorithm and linear interpolation.
But now I want to use a 44100 microphone. In real-time processing, My buffer is 256 points in 16000 Hz. So it is hard to find the input buffer size in 44100 Hz and downsample from 44100 to 16000.
When I used just decimation or average filter(https://github.com/mattdiamond/Recorderjs/issues/186), the output speech is higher then input and windowed sinc function interpolation makes a distortion.
is there any method to make 44100->16000 downsampling for realtime processing? please let me know...
thank you.
I had to implement a similar problem in the past, not for audio, but to simulate an asynchronism between a transmitte signal sampling frequency and a receiver sampling frequency.
This is how I will proceed:
Let us call T1 the sampling time duration of the incoming signal x: T1=1/44100 and
let us call T2 the sampling time duration of the signal to be generated y.
To calculate the value of the signal y[n*T2], select the two input values x[k*T1]and x[(k+1)*T2]
that surround the value to be calculated:
k*T1 <= n*T2 < (k+1)*T1
Then perform a linear interpolation from these two values. The interpolation factor must be recalculated for each sample.
If t = n*T2, a = k*T1 and b = (k+1)*T2, then
p = (x[b] - x[a])/T1
y[t] = p*(t-a) + x[a]
With a 44.1kHz frequency, x|a]and x[a+T1] should be rather well correlated, and the linear interpolation could be goood enough.
With the obtained quality is not good enough, you can interpolate the incoming signal with a fixed interpolation ratio,
for example 2, with a classical well defined good interpolation filter.
Then you can apply the previous procedure, with the help of the new calculated signal,
the sampling duration of which is T1/2.
If the incoming signal has some high frequencies, then, in order to avoid aliasing, you need to apply a low-pas filter to the incoming signal prior to the downsampling. Note that this is necessary even in your previous case 48kHz -> 16kHz
Related
I think most people know how to do numerical derivation in computer programming, (as limit --> 0; read: "as the limit approaches zero").
//example code for derivation of position over time to obtain velocity
float currPosition, prevPosition, currTime, lastTime, velocity;
while (true)
{
prevPosition = currPosition;
currPosition = getNewPosition();
lastTime = currTime;
currTime = getTimestamp();
// Numerical derivation of position over time to obtain velocity
velocity = (currPosition - prevPosition)/(currTime - lastTime);
}
// since the while loop runs at the shortest period of time, we've already
// achieved limit --> 0;
This is the basic building block for most derivation programming.
How can I do this with integrals? Do I use a for loop and add or what?
Numerical derivation and integration in code for physics, mapping, robotics, gaming, dead-reckoning, and controls
Pay attention to where I use the words "estimate" vs "measurement" below. The difference is important.
Measurements are direct readings from a sensor.
Ex: a GPS measures position (meters) directly, and a speedometer measures speed (m/s) directly.
Estimates are calculated projections you can obtain through integrating and derivating (deriving) measured values.
Ex: you can derive position measurements (m) with respect to time to obtain speed or velocity (m/s) estimates, and you can integrate speed or velocity measurements (m/s) with respect to time to obtain position or displacement (m) estimates.
Wait, aren't all "measurements" actually just "estimates" at some fundamental level?
Yeah--pretty much! But, they are not necessarily produced through derivations or integrations with respect to time, so that is a bit different.
Also note that technically, virtually nothing can truly be measured directly. All sensors get reduced down to a voltage or a current, and guess how you measure a current?--a voltage!--either as a voltage drop across a tiny resistance, or as a voltage induced through an inductive coil due to current flow. So, everything boils down to a voltage. Even devices which "measure speed directly" may be using pressure (pitot-static tube on airplane), doppler/phase shift (radar or sonar), or looking at distance over time and then outputting speed. Fluid speed, or speed with respect to fluid such as air or water, can even be measured via a hot wire anemometer by measuring the current required to keep a hot wire at a fixed temperature, or by measuring the temperature change of the hot wire at a fixed current. And how is that temperature measured? Temperature is just a thermo-electrically-generated voltage, or a voltage drop across a diode or other resistance.
As you can see, all of these "measurements" and "estimates", at the low level, are intertwined. However, if a given device has been produced, tested, and calibrated to output a given "measurement", then you can accept it as a "source of truth" for all practical purposes and call it a "measurement". Then, anything you derive from that measurement, with respect to time or some other variable, you can consider an "estimate". The irony of this is that if you calibrate your device and output derived or integrated estimates, someone else could then consider your output "estimates" as their input "measurements" in their system, in a sort of never-ending chain down the line. That's being pedantic, however. Let's just go with the simplified definitions I have above for the time being.
The following table is true, for example. Read the 2nd line, for instance, as: "If you take the derivative of a velocity measurement with respect to time, you get an acceleration estimate, and if you take its integral, you get a position estimate."
Derivatives and integrals of position
Measurement, y Derivative Integral
Estimate (dy/dt) Estimate (dy*dt)
----------------------- ----------------------- -----------------------
position [m] velocity [m/s] - [m*s]
velocity [m/s] acceleration [m/s^2] position [m]
acceleration [m/s^2] jerk [m/s^3] velocity [m/s]
jerk [m/s^3] snap [m/s^4] acceleration [m/s^2]
snap [m/s^4] crackle [m/s^5] jerk [m/s^3]
crackle [m/s^5] pop [m/s^6] snap [m/s^4]
pop [m/s^6] - [m/s^7] crackle [m/s^5]
For jerk, snap or jounce, crackle, and pop, see: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position.
1. numerical derivation
Remember, derivation obtains the slope of the line, dy/dx, on an x-y plot. The general form is (y_new - y_old)/(x_new - x_old).
In order to obtain a velocity estimate from a system where you are obtaining repeated position measurements (ex: you are taking GPS readings periodically), you must numerically derivate your position measurements over time. Your y-axis is position, and your x-axis is time, so dy/dx is simply (position_new - position_old)/(time_new - time_old). A units check shows this might be meters/sec, which is indeed a unit for velocity.
In code, that would look like this, for a system where you're only measuring position in 1-dimension:
double position_new_m = getPosition(); // m = meters
double position_old_m;
// `getNanoseconds()` should return a `uint64_t timestamp in nanoseconds, for
// instance
double time_new_sec = NS_TO_SEC((double)getNanoseconds());
double time_old_sec;
while (true)
{
position_old_m = position_new_m;
position_new_m = getPosition();
time_old_sec = time_new_sec;
time_new_sec = NS_TO_SEC((double)getNanoseconds());
// Numerical derivation of position measurements over time to obtain
// velocity in meters per second (mps)
double velocity_mps =
(position_new_m - position_old_m)/(time_new_sec - time_old_sec);
}
2. numerical integration
Numerical integration obtains the area under the curve, dy*dx, on an x-y plot. One of the best ways to do this is called trapezoidal integration, where you take the average dy reading and multiply by dx. This would look like this: (y_old + y_new)/2 * (x_new - x_old).
In order to obtain a position estimate from a system where you are obtaining repeated velocity measurements (ex: you are trying to estimate distance traveled while only reading the speedometer on your car), you must numerically integrate your velocity measurements over time. Your y-axis is velocity, and your x-axis is time, so (y_old + y_new)/2 * (x_new - x_old) is simply velocity_old + velocity_new)/2 * (time_new - time_old). A units check shows this might be meters/sec * sec = meters, which is indeed a unit for distance.
In code, that would look like this. Notice that the numerical integration obtains the distance traveled over that one tiny time interval. To obtain an estimate of the total distance traveled, you must sum all of the individual estimates of distance traveled.
double velocity_new_mps = getVelocity(); // mps = meters per second
double velocity_old_mps;
// `getNanoseconds()` should return a `uint64_t timestamp in nanoseconds, for
// instance
double time_new_sec = NS_TO_SEC((double)getNanoseconds());
double time_old_sec;
// Total meters traveled
double distance_traveled_m_total = 0;
while (true)
{
velocity_old_mps = velocity_new_mps;
velocity_new_mps = getVelocity();
time_old_sec = time_new_sec;
time_new_sec = NS_TO_SEC((double)getNanoseconds());
// Numerical integration of velocity measurements over time to obtain
// a distance estimate (in meters) over this time interval
double distance_traveled_m =
(velocity_old_mps + velocity_new_mps)/2 * (time_new_sec - time_old_sec);
distance_traveled_m_total += distance_traveled_m;
}
See also: https://en.wikipedia.org/wiki/Numerical_integration.
Going further:
high-resolution timestamps
To do the above, you'll need a good way to obtain timestamps. Here are various techniques I use:
In C++, use my uint64_t nanos() function here.
If using Linux in C or C++, use my uint64_t nanos() function which uses clock_gettime() here. Even better, I have wrapped it up into a nice timinglib library for Linux, in my eRCaGuy_hello_world repo here:
timinglib.h
timinglib.c
Here is the NS_TO_SEC() macro from timing.h:
#define NS_PER_SEC (1000000000L)
/// Convert nanoseconds to seconds
#define NS_TO_SEC(ns) ((ns)/NS_PER_SEC)
If using a microcontroller, you'll need to read an incrementing periodic counter from a timer or counter register which you have configured to increment at a steady, fixed rate. Ex: on Arduino: use micros() to obtain a microsecond timestamp with 4-us resolution (by default, it can be changed). On STM32 or others, you'll need to configure your own timer/counter.
use high data sample rates
Taking data samples as fast as possible in a sample loop is a good idea, because then you can average many samples to achieve:
Reduced noise: averaging many raw samples reduces noise from the sensor.
Higher-resolution: averaging many raw samples actually adds bits of resolution in your measurement system. This is known as oversampling.
I write about it on my personal website here: ElectricRCAircraftGuy.com: Using the Arduino Uno’s built-in 10-bit to 16+-bit ADC (Analog to Digital Converter).
And Atmel/Microchip wrote about it in their white-paper here: Application Note AN8003: AVR121: Enhancing ADC resolution by oversampling.
Taking 4^n samples increases your sample resolution by n bits of resolution. For example:
4^0 = 1 sample at 10-bits resolution --> 1 10-bit sample
4^1 = 4 samples at 10-bits resolution --> 1 11-bit sample
4^2 = 16 samples at 10-bits resolution --> 1 12-bit sample
4^3 = 64 samples at 10-bits resolution --> 1 13-bit sample
4^4 = 256 samples at 10-bits resolution --> 1 14-bit sample
4^5 = 1024 samples at 10-bits resolution --> 1 15-bit sample
4^6 = 4096 samples at 10-bits resolution --> 1 16-bit sample
See:
So, sampling at high sample rates is good. You can do basic filtering on these samples.
If you process raw samples at a high rate, doing numerical derivation on high-sample-rate raw samples will end up derivating a lot of noise, which produces noisy derivative estimates. This isn't great. It's better to do the derivation on filtered samples: ex: the average of 100 or 1000 rapid samples. Doing numerical integration on high-sample-rate raw samples, however, is fine, because as Edgar Bonet says, "when integrating, the more samples you get, the better the noise averages out." This goes along with my notes above.
Just using the filtered samples for both numerical integration and numerical derivation, however, is just fine.
use reasonable control loop rates
Control loop rates should not be too fast. The higher the sample rates, the better, because you can filter them to reduce noise. The higher the control loop rate, however, not necessarily the better, because there is a sweet spot in control loop rates. If your control loop rate is too slow, the system will have a slow frequency response and won't respond to the environment fast enough, and if the control loop rate is too fast, it ends up just responding to sample noise instead of to real changes in the measured data.
Therefore, even if you have a sample rate of 1 kHz, for instance, to oversample and filter the data, control loops that fast are not needed, as the noise from readings of real sensors over very small time intervals will be too large. Use a control loop anywhere from 10 Hz ~ 100 Hz, perhaps up to 400+ Hz for simple systems with clean data. In some scenarios you can go faster, but 50 Hz is very common in control systems. The more-complicated the system and/or the more-noisy the sensor measurements, generally, the slower the control loop must be, down to about 1~10 Hz or so. Self-driving cars, for instance, which are very complicated, frequently operate at control loops of only 10 Hz.
loop timing and multi-tasking
In order to accomplish the above, independent measurement and filtering loops, and control loops, you'll need a means of performing precise and efficient loop timing and multi-tasking.
If needing to do precise, repetitive loops in Linux in C or C++, use the sleep_until_ns() function from my timinglib above. I have a demo of my sleep_until_us() function in-use in Linux to obtain repetitive loops as fast as 1 KHz to 100 kHz here.
If using bare-metal (no operating system) on a microcontroller as your compute platform, use timestamp-based cooperative multitasking to perform your control loop and other loops such as measurements loops, as required. See my detailed answer here: How to do high-resolution, timestamp-based, non-blocking, single-threaded cooperative multi-tasking.
full, numerical integration and multi-tasking example
I have an in-depth example of both numerical integration and cooperative multitasking on a bare-metal system using my CREATE_TASK_TIMER() macro in my Full coulomb counter example in code. That's a great demo to study, in my opinion.
Kalman filters
For robust measurements, you'll probably need a Kalman filter, perhaps an "unscented Kalman Filter," or UKF, because apparently they are "unscented" because they "don't stink."
See also
My answer on Physics-based controls, and control systems: the many layers of control
I have a signal of frequency 10 MHz sampled at 100 MS/sec. How to compute FFT in matlab in terms of frequency when my signal is in rawData (length of this rawData is 100000), also
what should be the optimum length of NFFT.(i.e., on what factor does NFFT depend)
why does my Amplitude (Y axis) change with NFFT
whats difference between NFFT, N and L. How to compute length of a signal
How to separate Noise and signal from a single signal (which is in rawData)
Here is my code,
t=(1:40);
f=10e6;
fs=100e6;
NFFT=1024;
y=abs(rawData(:1000,2));
X=abs(fft(y,NFFT));
f=[-fs/2:fs/NFFT:(fs/2-fs/NFFT)];
subplot(1,1,1);
semilogy(f(513:1024),X(513:1024));
axis([0 10e6 0 10]);
As you can find the corresponding frequencies in another post, I will just answer your other questions:
Including all your data is most of the time the best option. fft just truncates your input data to the requested length, which is probably not what you want. If you known the period of your input single, you can truncate it to include a whole number of periods. If you don't know it, a window (ex. Hanning) may be interesting.
If you change NFFT, you use more data in your fft calculation, which may change the amplitude for a given frequency slightly. You also calculate the amplitude at more frequencies between 0 and Fs/2 (half of the sampling frequency).
Question is not clear, please provide the definition of N and L.
It depends on your application. If the noise is at the same frequency as your signal, you are not able to separate it. Otherwise, you can a filter (ex. bandpass) to extract the frequencies of interest.
How can I draw an spectrum for an given audio file with Bass library?
I mean the chart similar to what Audacity generates:
I know that I can get the FFT data for given time t (when I play the audio) with:
float fft[1024];
BASS_ChannelGetData(chan, fft, BASS_DATA_FFT2048); // get the FFT data
That way I get 1024 values in array for each time t. Am I right that the values in that array are signal amplitudes (dB)? If so, how the frequency (Hz) is associated with those values? By the index?
I am an programmer, but I am not experienced with audio processing at all. So I don't know what to do, with the data I have, to plot the needed spectrum.
I am working with C++ version, but examples in other languages are just fine (I can convert them).
From the documentation, that flag will cause the FFT magnitude to be computed, and from the sounds of it, it is the linear magnitude.
dB = 10 * log10(intensity);
dB = 20 * log10(pressure);
(I'm not sure whether audio file samples are a measurement of intensity or pressure. What's a microphone output linearly related to?)
Also, it indicates the length of the input and the length of the FFT match, but half the FFT (corresponding to negative frequencies) is discarded. Therefore the highest FFT frequency will be one-half the sampling frequency. This occurs at N/2. The docs actually say
For example, with a 2048 sample FFT, there will be 1024 floating-point values returned. If the BASS_DATA_FIXED flag is used, then the FFT values will be in 8.24 fixed-point form rather than floating-point. Each value, or "bin", ranges from 0 to 1 (can actually go higher if the sample data is floating-point and not clipped). The 1st bin contains the DC component, the 2nd contains the amplitude at 1/2048 of the channel's sample rate, followed by the amplitude at 2/2048, 3/2048, etc.
That seems pretty clear.
I write application where I must process digital signal - array of double. I must the signal decimate, filter etc.. I found a project gnuradio where are functions for this problem. But I can't figure how to use them correctly.
I need signal decimate (for example from 250Hz to 200Hz). The function should be similar to resample function in Matlab. I found, the classes for it are:
rational_resampler_base_fff Class source
fir_filter_fff Class source
...
Unfortunately I can't figure how to use them.
gnuradio and shared library I have installed
Thanks for any advice
EDIT to #jcoppens
Thank you very much for you help.
But I must process signal in my code. I find classes in gnuradio which can solve my problem, but I need help how set them.
Functions which I must set are:
low_pass(doub gain, doub sampling_freq, doub cutoff_freq, doub transition_width, window, beta)
where:
use "window method" to design a low-pass FIR filter
gain: overall gain of filter (typically 1.0)
sampling_freq: sampling freq (Hz)
cutoff_freq: center of transition band (Hz)
transition_width: width of transition band (Hz).
The normalized width of the transition band is what sets the number of taps required. Narrow –> more taps
window_type: What kind of window to use. Determines maximum attenuation and passband ripple.
beta: parameter for Kaiser window
I know, I must use window = KAISER and beta = 5, but for the rest I'm not sure.
The func which I use are: low_pass and pfb_arb_resampler_fff::filter
UPDATE:
I solved the resampling using libsamplerate
I need signal decimate (for example from 250Hz to 200Hz)
WARNING: I expressed the original introductory paragraph incorrectly - my apologies.
As 250 Hz is not related directly to 200 Hz, you have to do some tricks to convert 250Hz into 200Hz. Inserting 4 interpolated samples in between the 250Hz samples, lowers the frequency to 50Hz. Then you can raise the frequency to 200Hz again by decimating by a factor 4.
For this you need the "Rational Resampler", where you can define the subsample and decimate factors. Something like this:
This means you would have to do something similar if you use the library. Maybe it's even simpler to do it without the library. Interpolate linearly between the 250 Hz samples (i.e. insert 4 extra samples between each), then decimate by selecting each 4th sample.
Note: There is a Signal Processing forum on stackexchange - maybe this question might fall in that category...
More information: If you only have to resample your input data, and you do not need the actual gnuradio program, then have a look at this document:
https://ccrma.stanford.edu/~jos/resample/resample.pdf
There are several links to other documents, and a link to libresample, libresample4, and others, which may be of use to you. Another, very interesting, page is:
http://www.dspguru.com/dsp/faqs/multirate/resampling
Finally, from the same source as the pdf above, check their snd program. It may solve your problem without writing any software. It can load floating point samples, resample, and save again:
http://ccrma.stanford.edu/planetccrma/software/soundapps.html#SECTION00062100000000000000
EDIT: And yet another solution - maybe the simplest of all: Use Matlab (or the free Octave version):
pkg load signal
t = linspace(0, 10*pi, 50); % Generate a timeline - 5 cycles
s = sin(t); % and the sines -> 250 Hz
tr = resample(s, 5, 4); % Convert to 200 Hz
plot(t, s, 'r') % Plot 250 Hz in red
hold on
plot(t, tr(1:50)) % and resampled in blue
Will give you:
I am currently taking a class in school and I have to code FIR/IIR filter in C/C++.
As an input to the filter, 2kHz sine wave with white noise is used. Then, by inputting the sine wave to the C/C++ code, I need to observe the clean sine wave output. It's all done in software level.
My problem is that I don't know how to deal with this input/output of sine wave. For example, I don't know what type of file format I can use or need to use, I don't know how to make the sine wave form and etc.
This might be a very trivial question, but I have no clue where to begin.
Does anyone have any experience in this type of question or have any tips?
Any help would be really appreciated.
Generating the sine wave at 2kHz means that you want to generate values over time that, when graphed, follow a sine wave. Pick an amplitude (you didn't mention one), and pick your sample rate. See the graph here (http://en.wikipedia.org/wiki/Sine_wave); you want values that when plotted follow the sine wave graphed in 2D with the X axis being time, and the Y axis being the amplitude of the value you are measuring.
amplitude (volts, degrees, pascals, milliamps, etc)
frequency (2kHz, that is 2000 sine waves/second)
sample rate (how many samples do you want per second)
Suppose you generate a file that has a time value and an amplitude measurement, which you would want to scale to your amplitude (more on this later). So a device might give an 8-bit or 16-bit digital reading which represents either an absolute, or logarithmic measurement against some scale.
struct sample
{
long usec; //microseconds (1/1,000,000 second)
short value; //many devices give a value between 0 and 255
}
Suppose you generate exactly 2000 samples/second. If you were actually measuring an external value, you would get the same value every time (see that?), which when graphed would look like a straight line.
So you want a sample rate higher than the frequency. Suppose you sample as 2x the frequency. Then you would see points 180deg off on the sine wave, which might be peaks, up or down slope, or where sine wave crosses zero. A sample rate 4x the frequency would show a sawtooth pattern. And as you increase the number of samples, your graph looks closer to the actual sine wave. This is similar to the pixelization you see in 8-bit game sprites.
How many samples for any given sine wave would you think would give you a good approximation of a sine wave? 8? 16? 100? 500? Suppose you sampled 1,000,000 times per second, then you would have 1,000,000/2,000 = 500 samples per sine wave.
pick your sample rate (500)
define your frequency (2000)
decide how long to record your samples (5 seconds?)
define your amplitude (device measures 0-255, but what is measured max?)
Here is code to generate some samples,
#define MAXJITTER (10)
#define MAXNOISE (20)
int
generate_samples( long duration, //duration in microseconds
int amplitude, //scaled peak measurement from device
int frequency, //Hz > 0
int samplerate ) //how many samples/second > 0
{
long ts; //timestamp in microseconds, usec
long sdelay; //sample delay in usec
if(frequency<1) frequency1=1; //avoid division by zero
if(samplerate<1) samplerate=1; //avoid division by zero
sdelay = 1000000/samplerate; //usec delay between each sample
sample m;
int jitter, noise; //introduce noise here
for( long ts=0; ts<duration; ts+=sdelay ) // //in usec (microseconds)
{
//jitter, sample not exactly sdelay
jitter = drand48()*MAXJITTER - (MAXJITTER/2); // +/-1/2 MAXJITTER
//noise is mismeasurement
noise = drand48()*MAXNOISE - (MAXNOISE/2); // +/-1/2 MAXNOISE
m.usec = ts + jitter;
//2PI in a full sine wave
float period = 2*PI * (ts*1.0/frequency);
m.value = sin( period );
//write m to file or save me to array/vector
}
return 0; //return number of samples, or sample array, etc
}
First generate some samples,
generate_samples( 5*1000000, 100, 2000, 2000*50 );
You could graph the samples generated as a view of the noisy signal.
The above certainly answers many of your questions about how to record measurements, and what format is typically used. And it shows how transit through the period of multiple sine waves, generate random samples with jitter and noise, and record samples over some time duration.
Building your filter is a second issue. Writing the code to emulate the filter(s) described below is left as an exercise, or a second question as you glean more understanding,
http://en.wikipedia.org/wiki/Finite_impulse_response
http://en.wikipedia.org/wiki/Infinite_impulse_response
The generated sample of the signal (above) would be fed into the code you write to build the filter. Expect that the output of the filter would be a new set of samples, perhaps with jitter, but expect that your filter would eliminate at least some of the noise. You would then be able to graph the samples produced by the filter.
You might consider that converting the samples into a comma delimited file would enable you to load them into excel and graph them. And it might help if you elucidated your electronics background, your trig knowledge, and how much you know about filters, etc.
Good luck!