Problem Sheet 9 - ELEC309 Signal Processing and Digital Filtering PS9 Problem Sheet 9 1 a Design a High-pass IIR filter using the Butterworth

# Problem Sheet 9 - ELEC309 Signal Processing and Digital...

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ELEC309 Signal Processing and Digital Filtering PS9 1-2 Problem Sheet 9 1. a) Design a High-pass IIR filter using the Butterworth approximation and the Bilinear transformation with these characteristics. Sampling frequency F s = 32 KHz. Maximum attenuation of 0.5dB in the pass-band at f p = 12 KHz. Minimum attenuation of 40dB in the stop-band at f s = 2 KHz. i) Using the Bilinear transformation, 1 1 1 1 2 z z T s , find the pre-warped analogue frequencies corresponding to the pass-band and stop-band edge frequencies ii) Using the frequencies calculated in part (i) and the required attenuations, calculate the minimum order of the analogue filter. If you didn’t manage to calculate the pre - warped frequencies in part (i) then use the given edge frequencies in section a). iii) For N=3, calcula te Ω cH , the 3 dB frequency, in the Butterworth approximation for having exactly 0.5dB attenuation at Ω p .