Downsampling and anti-aliasing filters In lectures, we disucssed using an anti-a

Question

Downsampling and anti-aliasing filters In lectures, we disucssed using an anti-aliasing filter before sampling a continuous-time signal This is a low-pass filter with cut-off frequency (at most) the Nyquist frequency /T, rad/second (where T, is the sampling period). A variation on this idea is used when we down-sample a discrete-time signal Let rs be a discrete-time signal obtained by sampling a continuous-time signal with sampling period T. If we downsample rs by a factor of L to get ads[n] -rs[nL], then the new signal could have equivalently been obtained by sampling the continuous-time signal with sampling period LTs If we were to design an anti-aliasing filter to use before sampling with sampling period LTs we would ensure its cut-off frequency were at most /(LZ) rad/second (the corresponding Nyquist frequency). Instead, in this lab we will design a discrete-time anti-aliasing filter that will be used before we downsample rs by a factor of L to obtain rds. We want this discrete-time anti-aliasing filter to have cut-off frequency that corresponds to the continuous-time frequency n/(LT,). In other words, the maximum cutoff frequency should be /L rad/sample Prelab question 3 Suppose T8-1/44100 and L-5. What should be the maximum cut-off frequency of the anti-aliasing filter we use before downsampling? Express your answer as a fraction of (correct to one decimal place). In other words, if the desired cutoff frequency is WT rad/sample, enter W as your answer

Explanation / Answer

Max Cut off frequency= /LTs rad/second

                         =44100/5    

                          = 8820 rad/second.

or

Max cutoff frequency = /L rad/sample

                        = /5

                        =0.2 rad/sample

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