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Digital Signal Processing

Digital Signal Processing. Abbreviated by “DSP”. DSP System. Signal Voltage. Signal Voltage. Bits. Bits. ADC. DAC. Computer. ADC = Analog to Digital Converter DAC = Digital to Analog Converter. Benefits of DSP. More Flexibility

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Digital Signal Processing

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  1. Digital Signal Processing • Abbreviated by “DSP”

  2. DSP System Signal Voltage Signal Voltage Bits Bits ADC DAC Computer ADC = Analog to Digital Converter DAC = Digital to Analog Converter

  3. Benefits of DSP • More Flexibility • Computer software is easier to modify and change than electrical circuits • Improved performance • take advantage of powerful computer technology

  4. Sampling V(t) time Ts Ts = Sampling Period (time between samples) fs = Sampling Rate = 1/Ts (Hz or samples/second)

  5. Sampling Rate • What should it be? • If it is too low, the samples will not faithfully represent the signal • The Nyquist Sampling Theorem tells us how to sample

  6. Nyquist Sampling Theorem • fs >= 2*fmax • fmax is the highest frequency component of the signal • fmax is found by looking at the Power Spectrum and is identified as the highest frequency which power is non zero • fmax is also referred to as the Nyquist frequency

  7. Evaluating the Nyquist Sampling Theorem • Step one: Get the Power Spectrum • Step two: Find/Estimate fmax by looking at the Power Spectrum • Step Three: Multiply fmax by 2 and that is fs. fs can be this value or higher

  8. Practical Example: Modem Signal (PSK) and Noise fmax • fmax is estimated from Power Spectrum • fs should be Fmax muliplied by 2 or higher

  9. Other Examples • See Textbook Examples 3.10 and 3.11 (Page 60) for audio and music examples

  10. Aliasing • When fs is chosen less than 2*fmax (the Nyquist Criteria has not been met), the samples are not a faithful representation of the original signal. This effect is called aliasing and can lead to very misleading results • See Textbook Figure 3.14 (Page 63) for illustration

  11. DSP Example: Noise Removal Problem: Noise is introduced in a telephone line as a BFSK modem signal is transmitted. The presence of noise degrades the performance of the receiving demodulator Solution: Remove the noise by: a) Convert the received signal to digital bits (ADC) b) Run a computer program on the digitized bits and remove the noise c) Convert the processed bits back to analog (DAC) d) Forward this signal to the demodulator

  12. Original BFSK Modem Signal V(t) t

  13. BFSK Signal and Noise V(t) t • Noise is introduced in the channel • The presence of noise degrades demodulator performance

  14. BFSK Signal after Processing V(t) t • Noise is removed by “smart” computer program • Demodulator will be more successful with this signal

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