In this example, we do windowed-sinc FIR filter design using ScopeFIR.
Windowed-Sinc filters are based on the idea that a “brick-wall” filter in the Frequency domain corresponds to a “sinc” function (sin x / x) function in the Time domain. However, sinc functions have infinite length. Therefore, the sinc function needs to be truncated to form the coefficients of a Finite Impulse Response (FIR) filter. ScopeFIR’s Windowed Sinc filter design method simply designs a brick-wall filter with the corner frequencies you specify, then uses one of its standard data windows to truncate the filter to the specified length.
Although less flexible than the ScopeFIR’s Parks-McClellan FIR filter design method, the Windowed-Sinc method can produce filters which have flatter passbands or stopbands, for a given number of taps.
ScopeFIR’s Windowed-Sinc Specification Editor is shown below:
This filter is similar to the band-pass filter example designed with ScopeFIR’s Advanced Specification Editor. It uses the same Sampling Frequency, Number of Taps, and the same passband frequencies. It uses the Kaiser-Bessel window with an “Alpha” of 1.
The frequency response of the filter is shown below:
Compared to the frequency response of the band-pass filter example, this one has a much flatter passband and even has more stopband attenuation, although it does not transition between passband and stopband as quickly.
Our next example demonstrates a totally different filter, the Raised Cosine, which is commonly used in digital communications applications: