For a signal that is time limited to 10 ms and has an essential bandwidth of 10 KHz, determine , the number of signal samples necessary to compute a power-of-2 FFT with a frequency resolution of 50 Hz. Explain whether any zero padding is necessary.

500000 samples

zero padding is necessary.

Explanation: To determine the number of signal samples

Time = 10ms with bandwidth of 10kHz

Number of sample = 10×10^3×50

Number of sample = 5000000

The two reasons to zero pad are:

1). We must consider speed. A sample size that is a power of two is going to be the fastest possible. A sample size that is factorizable into small primes is a little slower. A prime number is slowest. However, for modern computers and a sample size on the order of 10,000

Now, if you want to do 100,000,000 sample sizes, then maybe it makes a difference.

2).The second reason to zero pad an FFT is to a little better frequency resolution.