Fourier Transforms and the DTFT
Stub. Applications of linear system models, sinusoidal signals as LTI eigenfunctions, the continuous-time Fourier transform, the discrete-time Fourier transform (DTFT), its properties, and the frequency response of an LTI system.
Sinusoids (and complex exponentials) are eigenfunctions of LTI systems — a sinusoid in, a scaled/phase-shifted sinusoid of the same frequency out — which is why decomposing a signal into sinusoids (a Fourier transform) is the natural complement to the time-domain convolution picture. Covers the continuous-time Fourier transform, its discrete-time analogue (the DTFT, the z-transform restricted to the unit circle), the DTFT’s properties, and the frequency response as the DTFT of the impulse response — the frequency domain’s version of the transfer function.
Outline (TODO — flesh out each)
- Applications of linear system models
- Sinusoidal signals as eigenfunctions of LTI systems
- The (continuous-time) Fourier transform
- The discrete-time Fourier transform (DTFT)
- Properties of the DTFT
- Frequency response of an LTI system