Question

I want to make a FIR filter using a window function. I have some sample data and size variable is a count of samples. The windowSize variable is a size of the window function.
At first I create the window function (blackman window): the variable window
Then I need to multiply it by sin(x) / x function and convolve with real data (variable data):

for (int i = 0; i < size; ++i) {
for (j = 0; j < windowSize; ++j) {
    double arg = 2.0 * PI * ((double)j - (double)windowSize / 2.0) / (double)windowSize;
    if (i + j - windowSize / 2 < 0)
       continue;
    if (arg == 0) {
    filteredData[i] += data[i + j - windowSize / 2] * window[j] * 1.0 /  (double)windowSize;
    } else
        filteredData[i] += data[i + j - windowSize / 2] * window[j] * (sin(arg) / arg) / (double)windowSize;
    }
}

The problem:

1. As a result I get a filtered data with an average which very different than the average of the original data. Where is a mistake?

2. In the DSP book it is written that in order to make a FIR filter we should multiply the function sin(x) / x by a window function and then perform the convolution, but nothing is written about x in the sin(x) / x, so I used the:

   double arg = 2.0 * PI * ((double)j – (double)windowSize / 2.0) / (double)windowSize;

for the x value, the argument of sine, is it correct?

Answer 1

The sin(x)/x filter is a lowpass filter. That is, it suppresses all frequencies above a certain cutoff frequency.

If the sampling frequency is Fs (Hertz) and you want a cutoff frequency of fc (Hertz), You should be using x = 2*PI*fc/(2*Fs)*n where n goes from -N to +N and N is large enough that the sin(x)/x function is close to zero. Don’t forget that sin(x)/x is 1 when x is zero.

To maintain the average of the signal you have to normalize the filter coefficients by their sum. I.e., set f_norm[k] = f[k] / sum(f[k], k=…)

That’s all I have to say at this point. It seems like you have a lot to learn. I suggest a good book on signal processing.