Figure shows the block diagram of a real-time spectrum analyzer working on the principle of frequency modulation. The given signal g (t) and a frequency-modulated signal s (t) are applied to a multiplier and the output g (t) s (t) is fed into a filter of impulse response b (t). The s (t) is linear FM signals whose instantaneous frequencies vary linearly with time at opposite rates, as shown by s (t) = cos (2??_ct ? ?kt²), b (t) = cos (2??_ct + ?kt²), where k is a constant. Show that the envelope of the filter output is proportional to the magnitude spectrum of the input signal g (t) with kt playing the role of frequency ?.

Transcribed Image Text:

gle) Filter Output