EE5410 Signal Processing --ideal frequency-selective filters
1. The class of frequency-selective filters , ie., LTI systems with frequency response chosen so as to pass one or several bands of frequencies with little or NO attenuation and to STOP or significantly attenuate frequencies outside those bands.
2. ideal lowpass filters have perfect frequency selectivity. That is, they pass without attenuation all frequencies at or lower than the cutoff frequency wc and completely stop all frequencies in the stopband (ie., higher than wc).
3. Moreover, these filters have zero phase characteristics, so they introduce NO phase distortion.
4. If the ideal frequency response is augmented with a linear phase characteristics, the impulse response is simply DELAYED buy an amount equal to the negative of the slope of this phase function.
5. The width of the filter passband is proportional to wc, while the width of the main lobe of the impulse is proportional to 1/wc.
6. As the bandwidth of the filter increases, the impulse response becomes narrower, and vice versa, consistent with the INVERSE relationship betweem time and frequency.