Subject : Signals & Systems

Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT).

Difficulty: Medium

Time scaling:

Compression of a signal in time domain is equivalent to expansion in frequency domain and vice versa. Proof:

Proof: $Y(ω)=\int_{-∞}^∞ y(t) e^{-jωt} \, dτ$

$Y(ω)=\int_{-∞}^∞ x(at) e^{-jωt} \, dτ$

Put at = τ then t = τa ∴dt = 1a dτ and limits will remain same …