Lowpass Highpass Frequency Transformation Technique

Question

• Show that the z → -z^-1 frequency transformation coverts a lowpass filter H_L(z) to a highpass filter

H_H(z) = H_L(-z^-1)

• The speech scrambler utilizes the modulation sequence [+1, -1, +1, -1, +1, -1, +1, -1,…] for the redistribution of frequency components. The z → -z^-1 is a lowpass-highpass frequency transformation technique. Compare these two methods and identify the similarities and differences.

Summary: This question belongs to Fourier series in engineering mathematics and discusses about frequency transformation that coverts a lowpass filter to a highpass filter.

Total word count: 162