**Desired Ideal Filter Response**

Unlike the design of IIR filters, the design of FIR
filters starts from the spectrum of the desired filter in the
DTFT domain. Let

**Windowing of Impulse Response**

To obtain an FIR filter approximating the frequency response
of the desired ideal filter, we need to find a filter
impulse response a causal and finite

*boxcar window*given as

**Frequency Response of Windowed Impulse Response**

Because the multiplication by the window function in time domain corresponds to a convolution in the DTFT domain, we can easily visualize the spectrum of the designed FIR filter. Different window functions have different main lobe width and peak sidelobe heights. The width of the main lobe governs the property of the frequency transition at band edges. The height of the peak sidelobes is related to the oscillations near the transition frequencies.