Work for DSP Supervision 1

Please submit your work as a PDF by emailing it to mti20 [at] cam [dot] ac [dot] uk by 1830 on Thursday 23rd October. Please include any code samples and their output in the PDF, and also send them as a separate file so that I can run them.

  1. What is the magnitude ratio between two signals if the power difference is
    1. -6dB
    2. 3dB
    3. 20dB
  2. What is the absolute power of 3dBm signal? What is the absolute power of a -10dBW signal?
  3. Examples sheet exercises 1, 2 and 4.
  4. [Lyons 1.3] Under what assumption does the C code "PI=2*asin(1.0);" correctly define the constant pi?
  5. [Lyons 1.23] Consider a square wave s(t), whose fundamental frequency is f0, and amplitude is A. Continuous Fourier analysis allows us to express this as formula for question 5...
    1. Imagine applying s(t) to a filter that completely removes s(t)'s lowest frequency spectral component. Draw the time-domain waveform at the output of such a filter.
    2. Assume s(t) represents a voltage whose f0 fundamental frequency is 1Hz, and we wish to amplify that voltage to peak amplitudes of +/-2A. Over what frequency range must an amplifier operate (that is, what must be the amplifier's passband width) in order to exactly double the ideal 1Hz squarewave's peak-peak amplitude?
  6. Pick any two of examples sheet exercises 3, 5, 6 and 7.
  7. Why is it usual to apply an analogue bandpass filter to a signal before bandpass sampling? Answer quantitatively if you can.
  8. Exam Question -- 2012 Paper 8 Question 6
    .