Question

a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given c, h[3] - b and h[4]-a. Prove that this by: h[0] - a, h[1]- b, h[2] FIR filter has a linear phase Design a length-5 Type-1 FIR filter having a zero at 2 +j2. Hence, find all the other zeros and provide the filter transfer function He) Draw a direct form realisation of the FIR filter given of part ii) above ii) iii) c) Windowing based FIR filter design technique is used to truncate the impulse response of an ideal zero-phase filter to obtain a finite impulse response. Design a causal FIR low-pass filter of length 5, with cut-off frequency of 400 Hz for a sampling rate of 4 kHz by using a rectangular window. Hence, find the five impulse response samples of the filter

Answer 1

valuoj. 外, HCe LP

ts half ste

Huen