1.) Three separate tones must be extracted from a noisy signal. The frequencies of the tones are 100 Hz, 300 Hz, and 450 Hz. The sampling rate is 1 kHz. Describe a low pass, a band pass, and a high pass filter that could be used to detect the individual tones. The cut-off frequency (or frequencies) for each filter should be 50 Hz from the tone it must detect. Identify the filter types, the cut-off frequencies, and the bandwidths.
2.) The impulse response of a filter is given by h[n]=delta[n-1]-0.28[n-2].
The input to the filter is x[n]=u[n]-u[n-7].
a.) Find the output.
b.) In (a), identify those output samples influenced by boundary effects.
3.) If the bandwidth of a low pass filter is 2 kHz, what is its cut-off frequency?