Convolution on one card: the exam cheat sheet

Lesson notes

Key points

• LTI system: A system that is linear and time-invariant, so convolution fully describes it.
• Impulse response h[n]: The output when the input is a single unit impulse; it characterises the system.
• y[n] = Σ x[k]h[n−k]: Convolution: flip h, shift it, multiply with x, then sum the products.
• Output length: Convolving lengths N and M gives an output of length N plus M minus one.
• Convolution theorem: Convolution in time equals multiplication of the spectra in frequency.
• Correlation vs convolution: Correlation skips the flip; for symmetric kernels both give the same result.

Takeaway: Flip, shift, multiply, sum: that is convolution.