Practical skill-building

Fourier Practice Set

Use these 10 problems to prep for quizzes, labs, and interviews. Each question includes a short hint to keep you moving.

Problems

Given samples from a 1000 Hz system, identify the dominant frequency from the FFT bins. Hint: frequency resolution is fs/N.

A 900 Hz tone sampled at 1 kHz appears as what frequency? Hint: fold around Nyquist.

For leakage reduction in short signals, compare rectangular and Hann windows. Hint: think sidelobes.

Two signals have same magnitude spectrum but different phase. How can waveforms differ?

Choose a filter to remove 60 Hz hum while preserving speech content.

Explain what convolution means physically for an LTI system impulse response.

Describe what it means when harmonics spread over time in a spectrogram.

Select minimum sampling rate for a band-limited signal up to 3.2 kHz.

For N=256, fs=2048 Hz, what frequency is bin 37?

Your FFT shows unexpected low-frequency energy. List three likely causes and test steps.