c++ butterworth

Butterworth is a surname that originated in England. It is derived from the Old English words "butter," meaning butter, and "worth," meaning homestead or farm. The name likely referred to someone who lived or worked on a butter farm or who sold butter. The name Butterworth is most commonly found in the northern part of England, particularly in Lancashire and Yorkshire.

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butterworthfilter c++

Butterworth filter is a type of electronic filter designed to have a frequency response that is as flat as possible in the passband. It is a type of low-pass filter that attenuates the high-frequency signals and passes the low-frequency signals. The Butterworth filter is named after the British engineer Stephen Butterworth, who first described the filter in 1930.

In C programming language, the Butterworth filter can be implemented using various libraries such as the Signal Processing Toolbox in MATLAB or the scipy.signal library in Python. The following is a sample code for implementing the Butterworth filter in C.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define PI 3.141592653589793

double butterworth_filter(double input_signal, double *coefficients, double *delay_line, int order)
{
int i;
double output_signal = 0.0;

// Shift delay line
for (i = order - 1; i >= 1; i--)
{
delay_line[i] = delay_line[i - 1];
}

// Add input signal to delay line
delay_line[0] = input_signal;

// Calculate output signal
for (i = 0; i < order; i++)
{
output_signal += coefficients[i] * delay_line[i];
}

return output_signal;
}

int main()
{
double sample_rate = 1000.0; // Hz
double cutoff_frequency = 50.0; // Hz
double nyquist_frequency = sample_rate / 2.0;
double normalized_cutoff_frequency = cutoff_frequency / nyquist_frequency;
int order = 4; // Filter order

// Calculate filter coefficients
double *coefficients = (double*)malloc(order * sizeof(double));
int i;
for (i = 0; i < order; i++)
{
double theta = PI / 2.0 + (2.0 * i + 1.0) * PI / (2.0 * order);
coefficients[i] = sin(theta);
}
double gain = pow(cos(PI / 4.0), order);
for (i = 0; i < order; i++)
{
coefficients[i] /= gain;
}

// Initialize delay line
double *delay_line = (double*)calloc(order, sizeof(double));

// Filter input signal
double input_signal = 0.0;
double output_signal = 0.0;
for (i = 0; i < 1000; i++)
{
input_signal = sin(2.0 * PI * 10.0 * i / sample_rate);
output_signal = butterworth_filter(input_signal, coefficients, delay_line, order);
printf("%f\n", output_signal);
}

free(coefficients);
free(delay_line);

return 0;
}

c++ butterworthfilter

Butterworth filter is a type of linear filter used in signal processing to remove unwanted noise and maintain the frequency content of the signal. It is a type of low-pass filter that attenuates high-frequency components of the signal while allowing low-frequency components to pass through. The Butterworth filter has a flat frequency response in the passband and a gradual roll-off in the stopband. It is named after the British engineer and mathematician Stephen Butterworth, who first described it in 1930. The Butterworth filter is widely used in various applications, including audio processing, image processing, and communication systems.