To send high frequency signals to the smaller tweeter speaker in an audio amplifier, a high-pass filter has to be designed by using the Butterworth approximation, according to the following specifications: The cutoff frequency fc is chosen at 1 kHz with a minimum attenuation Amin of 20 dB at fs = 500 Hz

a) Determine the order of the filter to comply with the previous specifications by using frequency normalization and the high-pass to low-pass transformation.