sergeyhaki
commented
1 year ago The Hilbert Transform is a digital signal processing algorithm that can be used to generate an analytic signal, which has a complex envelope that can be used for various signal processing tasks. Here is a sample implementation of the discrete-time Hilbert transform for AVR MCU (ATmega328P) using int16_t data type:
include <avr/io.h>
include // for the sin() function
// parameters
define N 64 // number of samples
define PI 3.14159265358979323846
int16_t signal[N]; // input signal int16_t envelope[N]; // envelope of the signal using Hilbert transform
int main(void) { // generate input signal for (int i = 0; i < N; i++) { signal[i] = 1000 sin(2 PI * i / N); }
// compute Hilbert transform
int16_t hilbert[N];
for (int n = 0; n < N; n++) {
hilbert[n] = 0;
for (int k = 0; k < N; k++) {
hilbert[n] += signal[k] * sin(2 * PI * (n - k) / N) * (2.0 / N);
}
}
// compute envelope
for (int i = 0; i < N; i++) {
envelope[i] = sqrt(signal[i] * signal[i] + hilbert[i] * hilbert[i]);
}
// do something with the envelope
return 0;}
The program starts by generating a test input signal that consists of a 1kHz sine wave with a peak amplitude of 1000. The signal is stored in an array signal . The program then computes the Hilbert transform by iterating over each sample n of the output signal and summing up the contributions from all samples k of the input signal. The formula used is:
H[n] = 1/N sum_{k=0}^{N-1} x[k] sin(2 pi (n-k) / N)
Where x is the input signal. The result is stored in an array hilbert .
The program then computes the envelope of the signal by taking the magnitude of the complex analytic signal represented by signal and hilbert . The formula used is:
env[n] = sqrt(x[n]^2 + H[n]^2)
The result is stored in an array envelope .
Finally, the program can do something with the envelope, such as display it on a display or use it for further processing. Note that this implementation is just a sample and may not be optimal or suited for all applications.
/ To implement a 3rd order all-pass filter on an AVR MCU using int32_t data types, you can use the following code: /
include
define SCALE_FACTOR 32768
int32_t allPassFilter3rdOrder(int32_t input, int32_t* delayLine) { int32_t output;
}
/ This function takes an input sample as an int32_t and a pointer to a delay line array, which should have a length of 2. The function returns the filtered output as an int32_t.The coefficients for a 3rd order all-pass filter are defined as constant variables using the SCALE_FACTOR of 32768. The output is calculated using these coefficients and the input sample, as well as the current and previous values in the delay line buffer.To use this function, you would call it in your main program loop, passing in the input sample and the delay line array. The filter will update the delay line with the new output value and return the filtered output. /