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COLOURED NOISE REMOVAL AND    EQUALISING THE CHANNEL EFFECT    FROM A NOISY AUDIO SIGNAL             G. Anudeep Reddy (EC0...
INTRODUCTION   We want to transmit a song signal.        Song Signal            Transmitter        Loud Speaker          ...
REMOVAL OF NOISE   The signal may be corrupted by Noise.     Song                    Transmitter         Noise     Signal...
REMOVAL OF NOISE   The signal may be corrupted by Noise.     Song                    Transmitter         Noise     Signal...
WHITE NOISE   White noise is a signal (or process), having    equal power in any band of a given bandwidth    (power spec...
COLORED NOISE   Based on Spectral density (power distribution    in the frequency spectrum) we can distinguish    differe...
COLORED NOISE   The color names for these different types of    sounds are derived from a loose analogy    between the sp...
PINK NOISE   Similar to White Noise except the power    density decreases 3 dB per octave as the frequency    increases. ...
BLUE NOISE   Similar to White Noise except the power    density increases 3 dB per octave as the frequency    increases. ...
GENERATION OF COLORED NOISE Colored noise can be generated by passing the  white noise through a shaping filter. The res...
REMOVAL OF CHANNEL EFFECT   The signal may be corrupted by channel    transfer function also.    Song               Trans...
REMOVAL OF CHANNEL EFFECT   The signal may be corrupted by channel    transfer function also.    Song               Trans...
EQUALIZER   The equalizer should have transfer function    which is inverse of channel.                          1       ...
COMPLETE BLOCK DIAGRAM                         14
CHANNEL AND CHANNEL EQUALIZERo A finite impulse response (FIR) filter is a type of asignal processing filter whose impulse...
o FIR filters can be discretetime or continuous-time, and digital or analog.                                              ...
 For a discrete-time FIR filter, the output is aweighted sum of the current and a finite number ofprevious values of the ...
o Similarly the equalizer can be considered as an FIRfilter(discrete time, digital FIR filter)  From the block diagram, i...
AN ADAPTIVE LINEAR EQUALIZER                         xk-1               xk-2                     xk-L+1      xk         Z-...
ADAPTIVE LINEAR EQUALIZERo A procedure for adjusting or adopting the weights iscalled weight adjustment or adaptation proc...
If the weight and input vectors are expressed as                                              T       Xk    [ x0 k   x1 k ...
LEARNING ALGORITHMS LMS  Algorithm RLS Algorithm Kalman Filter Neural Algorithm Fuzzy Logic System Optimization Algo...
LEAST MEAN SQUARE ALGORITHM❏ LMS: adaptive filtering algorithm having  two basic processes  ✔ Filtering process, producing...
LEAST MEAN SQUARE ALGORITHMo LMS algorithm is one of the conventionaltechniques applied to channel equalization. The costf...
o The equalizer filters impulse response vector isadapted using the following equation,    w(k+1) = w(k) + 2µ.e(k).x(k)   ...
STABILITY OF LMS   More practical test for stability is                                2              0                  ...
xk-1                       xk-2                       xk-L+1      xk                        Z-1                        Z-1...
LMS BLOCK DIAGRAM              a0x(k)       Z-1    a1       Z-1              a2         y (k)       +                     ...
NUMERICAL EXAMPLE- CHANNEL EQUALIZATION❏ Transmitted signal: random sequence of  ±1‟s.❏ The transmitted signal is corrupte...
❏ The amplitude distortion, and eigen value spread,were controlled by W. The received signal is processed by a linear, 11...
31
REFERENCES   “Digital Signal Processing using MATLAB” demos    by Charulatha Devi.   Georgi Illiev and Nikola Kasabov, "...
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Dsp ppt madhuri.anudeep

  1. 1. COLOURED NOISE REMOVAL AND EQUALISING THE CHANNEL EFFECT FROM A NOISY AUDIO SIGNAL G. Anudeep Reddy (EC08484)1 G. Madhuri (EC08485)
  2. 2. INTRODUCTION We want to transmit a song signal. Song Signal Transmitter Loud Speaker Receiver 2
  3. 3. REMOVAL OF NOISE The signal may be corrupted by Noise. Song Transmitter Noise Signal Receiver 3
  4. 4. REMOVAL OF NOISE The signal may be corrupted by Noise. Song Transmitter Noise Signal Loud Filter Receiver Speaker 4
  5. 5. WHITE NOISE White noise is a signal (or process), having equal power in any band of a given bandwidth (power spectral density). 5
  6. 6. COLORED NOISE Based on Spectral density (power distribution in the frequency spectrum) we can distinguish different types of noise. This classification by spectral density is given "color" terminology, with different types named after different colors. 6
  7. 7. COLORED NOISE The color names for these different types of sounds are derived from a loose analogy between the spectrum of frequencies of sound wave present in the sound and the equivalent spectrum of light wave frequencies. That is, if the sound wave pattern of "blue noise" were translated into light waves, the resulting light would be blue, and so on. 7
  8. 8. PINK NOISE Similar to White Noise except the power density decreases 3 dB per octave as the frequency increases. In technical terms the density is inversely proportional to the frequency. 8
  9. 9. BLUE NOISE Similar to White Noise except the power density increases 3 dB per octave as the frequency increases. In technical terms the density is proportional to the frequency. 9
  10. 10. GENERATION OF COLORED NOISE Colored noise can be generated by passing the white noise through a shaping filter. The response of the colored noise can be varied by adjusting the parameters of the shaping filter. White Shaping Colored Noise Filter Noise 10
  11. 11. REMOVAL OF CHANNEL EFFECT The signal may be corrupted by channel transfer function also. Song Transmitter Channel Noise Signal Receiver 11
  12. 12. REMOVAL OF CHANNEL EFFECT The signal may be corrupted by channel transfer function also. Song Transmitter Channel Noise Signal Loud Filter Equalizer Receiver Speaker 12
  13. 13. EQUALIZER The equalizer should have transfer function which is inverse of channel. 1 H (z) C (z) Where H(z) is the transfer function of equalizer and C(z) is the transfer function of channel. But in most of the cases we do not know the transfer function of the channel, so we will adapt the equalizer transfer function using Learning algorithm. 13
  14. 14. COMPLETE BLOCK DIAGRAM 14
  15. 15. CHANNEL AND CHANNEL EQUALIZERo A finite impulse response (FIR) filter is a type of asignal processing filter whose impulse response (orresponse to any finite length input) is of finite duration,because it settles to zero in finite time.o This is in contrast to infinite impulse response (IIR)filters, which have internal feedback and may continueto respond indefinitely (usually decaying).o The impulse response of an Nth-order discrete-timeFIR filter, lasts for N+1 samples, and then dies to zero. 15
  16. 16. o FIR filters can be discretetime or continuous-time, and digital or analog. 16
  17. 17.  For a discrete-time FIR filter, the output is aweighted sum of the current and a finite number ofprevious values of the input. The operation isdescribed by the following equation, which defines theoutput sequence y[n] in terms of its inputsequence x[n]:o The channel can be considered as a discretetime digital FIR filter 17
  18. 18. o Similarly the equalizer can be considered as an FIRfilter(discrete time, digital FIR filter)  From the block diagram, it is evident that the optimal equalizer should have transfer function which is inverse of channel. Hence channel equalization is also known as inverse filtering. Transfer function of Channel , C(z)= b0+ b1z-1+ b2z-2 + bnz-n Transfer function of the Equalizer, H(z)= 1/C(z) 18
  19. 19. AN ADAPTIVE LINEAR EQUALIZER xk-1 xk-2 xk-L+1 xk Z-1 Z-1 Z-1 w0k w1k w2k w(L-1)k ∑ ykThere is an input signal vector, x 0 , x1 ... x L 1a corresponding set of adjustable weights, w 0 , w1 ... w L 1 19a summing unit, and a single out put signal.
  20. 20. ADAPTIVE LINEAR EQUALIZERo A procedure for adjusting or adopting the weights iscalled weight adjustment or adaptation procedure.o The combiner is called linear because for fix setting ofweights its output is a linear combination of the inputcomponents.o The output of the combiner can be represented as L yk w lk x k l l 0 where w lk denotes l th weight at k th instant. 20
  21. 21. If the weight and input vectors are expressed as T Xk [ x0 k x1 k  x ( L 1) K ] T Wk [ w0 k w1 k  w ( L 1) K ] then the output is given by T yk xk wk The weights of the combiner are to be updated using various learning algorithms Ravi Kumar Jatoth Department 21 of ECE NITW
  22. 22. LEARNING ALGORITHMS LMS Algorithm RLS Algorithm Kalman Filter Neural Algorithm Fuzzy Logic System Optimization Algorithms All the algorithms update the weights of the equalizer using different cost functions. 22 Ravi Kumar Jatoth Department of ECE NITW
  23. 23. LEAST MEAN SQUARE ALGORITHM❏ LMS: adaptive filtering algorithm having two basic processes ✔ Filtering process, producing 1) output signal 2) estimation error ✔ Adaptive process, i.e., automatic adjustment of filter tap weights 23
  24. 24. LEAST MEAN SQUARE ALGORITHMo LMS algorithm is one of the conventionaltechniques applied to channel equalization. The costfunction is Mean Square Error (MSE). It updates theweights of the adaptive FIR filter based on the errorobtained. The instantaneous error at any time-step kcan be represented as e(k) = d(k) – y(k)where d(k) delayed input reference is signal at time-step „k‟, and y(k)‟ is estimated output from equalizer. 24
  25. 25. o The equalizer filters impulse response vector isadapted using the following equation, w(k+1) = w(k) + 2µ.e(k).x(k) where µ is called „Convergence factor’ or ‘Learningrate parameter’, (0 ≤ µ ≤ 1). x(k) Is input from transmitter at time-step k.o This procedure is repeated till the Mean Square Error(MSE) of the network approaches a minimum value. 25
  26. 26. STABILITY OF LMS More practical test for stability is 2 0 input signal power Larger values for step size  Increases adaptation rate (faster adaptation)  Increases residual mean-squared error 26 351M Digital Signal Processing
  27. 27. xk-1 xk-2 xk-L+1 xk Z-1 Z-1 Z-1 w0k w1k w2k w(L-1)k ∑ ek yk LMS - Algorithm ∑ + dk Fig. 2 Adaptive filter using LMS algorithm TXk xk xk 1  xk L 1 the L-by-1 tap input vector. T 27Wk w0 k w1 k  w L 1 k the L-by-1 tap weight vector
  28. 28. LMS BLOCK DIAGRAM a0x(k) Z-1 a1 Z-1 a2 y (k) + ∑ ∑ e (k) - Z-1 a3 d(k) Z-1 a4 28 LMS
  29. 29. NUMERICAL EXAMPLE- CHANNEL EQUALIZATION❏ Transmitted signal: random sequence of ±1‟s.❏ The transmitted signal is corrupted by a channel.❏ Channel impulse response: 29
  30. 30. ❏ The amplitude distortion, and eigen value spread,were controlled by W. The received signal is processed by a linear, 11-tapFIR equalizer adapted with the LMS algorithm 30
  31. 31. 31
  32. 32. REFERENCES “Digital Signal Processing using MATLAB” demos by Charulatha Devi. Georgi Illiev and Nikola Kasabov, "Channel Equalization using Adaptive Filtering with Averaging", University of Otago, Newzeland. M Reuter, J Zedlier, "Nonlinear effects in LMS adaptive equalizers", IEEE Trans.Signal Processing, June1999. 32

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