Digital Signal Processing Summary
Upcoming SlideShare
Loading in...5

Like this? Share it with your network


Digital Signal Processing Summary

Uploaded on

3F3 – Digital Signal Processing (DSP), January 2009, lecture slides 8, Dr Elena Punskaya, Cambridge University Engineering Department

3F3 – Digital Signal Processing (DSP), January 2009, lecture slides 8, Dr Elena Punskaya, Cambridge University Engineering Department

More in: Education
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads


Total Views
On Slideshare
From Embeds
Number of Embeds



Embeds 312 286 24 1 1

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

    No notes for slide


  • 1. What you should know after these lectures? Elena Punskaya 1
  • 2. Introduction to DSP • Understand what is Digital Signal Processing • Be able to provide very briefly some examples of applications of DSP • Be able to state briefly main DSP limitations – aliasing (cannot distinguish between higher and lower frequencies, how to prevent – sampling theorem, correct reconstruction – antialias filter) – frequency resolution (sample for a limited period of time, does not pick up relatively slow changes) – quantisation error (sampling, loss of info, limited precision) • Be able to describe advantages of Digital over Analogue Signal Processing – reprogrammable / easily portable / duplicable – better control of accuracy – can be easily stored – precise mathematical operations 2
  • 3. DTFT and DFT • Be aware of time-domain and frequency-domain analyses • Be comfortable with performing fundamental operations for sampled signals – DTFT, Inverse DTFT • Be able to state main problems with computing DTFT on a computer, explain how they can be overcome to obtain DFT • Be able to derive DFT from DFTF – by taking DFTF of the windowed signal • Be able to derive – spectrum of the windowed signal – rectangular window spectrum • Be aware of – zero-padding – Inverse DFT, circular convolution – Use of DFT and IDFT to compute standard convolution and thus perform linear filtering 3
  • 4. FFT • Know the basic principles behind radix-2 FFT algorithms – N is a power of 2 – FFT butterfly structure – decomposition to reduce evaluation to single point DFT – bit reversal operations – in place computation – the number of computations required to compute one butterfly – the total number of stages required • Be able to show the total number of complex and real operation required to compute N-point FFT • Be able to demonstrate the efficiency of FFT compared to DFT (based on the total operations count) • Be able to five (briefly) examples of applications 4
  • 5. Basics of Digital Filters • Be very familiar with the main characteristics – time-domain linear difference equations filter’s unit-sample (impulse) response (linear convolution causal LTI) – frequency-domain more general, Z-transform domain – system transfer function – poles and zeros diagram in the z-plane (stability) Fourier domain – frequency response (distance to poles and zeros, close to pole – magnitude rises, close to zero – magnitude falls) – spectrum of the signal • Be able to state and identify on the diagram main elements of Digital Filters – adders/multipliers/delays/advances • Be able to state four basic ideal filter types – lowpass/high-pass/band-pass/band-stop and their main characteristics – magnitude response and linear phase response • Be able to explain briefly why it is impossible to implement an ideal filter – needs to be causal to be realised 5
  • 6. Design of FIR Filters • Know main characteristics – difference equation/transfer function/impulse response • Be aware of FIR using DFT and IDFT implementation • Know why linear phase filters are used/understand principles • Understand the window method for FIR filters – infinite response of the ideal filter and, hence, the need for truncation and shift to the right – truncation = pre-multiplication by rectangular window • a filter of large order has a narrow transition band • sharp discontinuity results in side-lobe interference – use of windows with no abrupt discontinuity can • Know how to use the window method for FIR filters (steps) • Be able to explain why the window method is not optimal – pass-band and stop-band parameters are equal thus unnecessary high accuracy in the pass band – the ripple of the window is not uniform – more freedom can be allowed Hence be able to give brief examples of other (optimal) methods of FIR filter design 6
  • 7. Design of IIR filters • Know main characteristics – difference equation/transfer function/impulse response/stability issue • Be familiar with the main concepts of impulse invariant, matched z- transform and backward difference method and their disadvantages • Be able to state main properties of bilinear transform – produces a digital filter whose frequency response has the same characteristics as the frequency response of the analogue filter – maps the Left half s-plane onto the interior of the unit circle in the z-plane, ensures stability • monotonic Ω↔ ω mapping Ω= 0 is mapped to ω = 0, and Ω = ∞ is mapped to ω = π (half the sampling frequency). • • mapping between the frequency variables • Know how to use bilinear transform to design IIR filters (steps) • Know how to design highpass/bandpass/bandstop filters using frequency transformation • Be able to state the main problem with bilinear transform – performs a nonlinear mapping of the phase leading to a distortion (or warping) of the digital frequency response – hence pre-warping 7
  • 8. Implementation of Digital Filters • Be able to compare IIR and FIR filters • Be able to state main concerns of filter implementation and ways of addressing them – Speed/power (+memory) • Be familiar with different forms of realization structures – Direct Form I/II – cascade/parallel/feedback and be able to briefly explain why they are of use • Be able to state the undesirable consequences of finite-precision filter implementation and explain the strategies for overcoming them – Overflow (scaling and saturation arithmetic) • Be familiar with roundoff (quantisation) noise generation, limit cycles and deadbands 8
  • 9. Thank you! 9