Tutorial: Windowed Sinc Filter Design

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 method of designing FIR filters, 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 Bandpass 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 Bandpass 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:

Raised Cosine Filter

Other FIR filter design examples:

• Simple Parks-McClellan Lowpass Filter
• Simple Parks-McClellan Highpass Filter
• Advanced Parks-McClellan Bandpass Filter

Download ScopeFIR for Windows XP/2000/ME/98/95

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