For the filter shown in Figure Q2 below: x[n] 1 |H(el)| 10-6cos(w) Find the filter gain in dB at frequencies of 0 and f./2. Plot the pole-zero diagram of the filter and comment on filter stability. b) Compare (numerically) the cost of computing 256-point DFT of a length-1024 signal, using a direct DFT, a pre-wrapped DFT and a pre-wrapped FFT. i) y[n] iii) ii) iii) Figure Q2 Show that the magnitude of the frequency response for this filter can be expressed as: c) It is required to design a digital audio system that stores audio data in a storage device (a hard disk). The length of audio data is one hour and the available disk space is 0.5 GB (Gigabytes). Will the available disk space be enough to store the required audio data? Prove your answer. [Hint: Assume the sampling rate is 44.1 kHz, and each sample is quantised with 16 bits]. d) Consider an echo system characterised by a round-trip travel time from the source to a reflecting object and a coefficient representing the reflection and propagation losses. Write down the difference equation of such system, find its transfer function and its poles and zeros. Derive and sketch its frequency response. Design a method to cancel the echo. State any assumptions.