The Discrete Cosine Transform

Human hearing is more sensitive to mid-range frequencies than to extremely high or low frequencies. Therefore we would like to quantize high and low frequencies at different quantization levels, i.e. use different numbers of bits to encode each frequency bin. To compress a signal $x[n]$, we can convert it to the frequency domain $X[n]$ using the DFT. Then we quantize each frequency bin with a different number of bits based on the frequency response of the human ear.