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Figure shows the block diagram of a real-time spectrum analyzer

Figure shows the block diagram of a real-time spectrum analyzer

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 (2pA?ct – pkt2), b (t) = cos (2pA?ct + pkt2), 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 A?.

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