Question

If the slow time signal is given by the 16 samples y[] = o (a) Derive the M-point Discrete-time Fourier Transform, Y(f), which is referred to as the digital sinc function

Answer 1

The M-point Discrete-time Fourier Transform of the slow time signal can be derived using the formula Y(f) = ∑(y[n] * e^(-j2πnf/M)), where n ranges from 0 to M-1 and f ranges from -0.5 to 0.5. By substituting the values of n and f into the formula, you can calculate the values of Y(f) at different frequencies.

Step-by-step explanation:

The M-point Discrete-time Fourier Transform of the slow time signal can be derived using the formula:

Y(f) = ∑(y[n] * e^(-j2πnf/M)), where n ranges from 0 to M-1 and f ranges from -0.5 to 0.5.

Since the given signal has 16 samples, M will be 16. By substituting the values of n and f into the formula, you can calculate the values of Y(f) at different frequencies. This will give you the digital sinc function Y(f) for the given slow time signal.