- Q3 A A Signal X N With Sampling Frequency Fs Is Upsampled Interpolated By A Factor 3 To Create A New Signal Y N W 1 (57.38 KiB) Viewed 26 times
Q3. (a) A signal x[n] with sampling frequency fs is upsampled (interpolated) by a factor 3 to create a new signal y[n] with sampling frequency 3fs. The upsampler uses a time domain zero interpolator followed by an ideal low pass digital filter with a gain of 3. Explain, using graphical illustrations, why the low pass filter is required and define the characteristics of the ideal low pass filter. 2 marks (b) A FIR low pass filter with impulse response h[n)=[ n[o] h[1] h[2] ..... h[8] ] is to be employed in the time domain signal interpolator described in part (a) above. Derive and draw a diagram of a polyphase realisation of h[n] using 3 polyphase FIR filters. 4 marks (c) Show how the Noble Identity for upsampling in digital filters can be used to form an efficient implementation of the digital upsampler (interpolators) described in part (a) and (b) above. 10 marks (d) Given that x[n] is a finite length signal of length 120, compute the relative computational savings made, in terms of multiplications only, in using the design described in part (a) [i.e. No Polyphase filter] with a LPF length of 9 to the upsampler defined in part (c) above. 4 marks