### Time, Frequency, and Time-Frequency

We know we can represent functions in terms of frequency components (sinusoids). These basis functions are nonzero at single points in the frequency domain, but never die out in the time domain.

We can also represent functions in the time domain. Using the sifting property, we can represent any function in terms of deltas.

For example, imagine every discrete time function as a train of appropriately scaled Kronecker deltas. These basis functions are single points in time, never dying out in frequency.

We can also represent functions in terms of other basis functions, somewhat localized in time and frequency, like the pulse and sinc.

These functions are referred to as wavelets, and they form time-frequency representation of a signal.

EECS 20 Chapter 10 Part 1