1 / 26

Digital Filtering

Digital Filtering. (1). Difference equation:. (2). Canonical Form:. Digital filtering. u k. y k. The Implementation in MATLAB. Coefficients of numerator and denominator:. Mux – multiplexer DeMux – demultiplexer; ASC- analog signals commutator;

takoda
Télécharger la présentation

Digital Filtering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Digital Filtering

  2. (1) Difference equation: (2) Canonical Form: Digital filtering uk yk

  3. The Implementation in MATLAB Coefficients of numerator and denominator:

  4. . . Mux – multiplexer DeMux – demultiplexer; ASC- analog signals commutator; ADC, DAC – analog-to-digital and digital-to-analog converters I/O Syst. – “input-output” system CPU – central processor unit CU – control unit ROM – read-only memory RAM – random access memory

  5. (3) Real poles: Complex poles (Second- order-sections (SOS)): (4) (5) (5) The series form of the filter programming: ‑ biquadratic filter ; (5a) + -

  6. . . . x y . . Parallel realization: (6)

  7. FIR and IIR Filters 1.FIR – filters – moving average process (7) (8) Example: Impulse input: Finite impulse response (FIR): 2.IIR – filters – “moving average + auto regression” – ARMA – process. (9)

  8. Impulse Response of the IIR filters (10) (11) b0 = w(0) ; b1- b0a1 = w(1) ; b2- a1b1+b0a21 = w(2) ; ……………………...

  9. Theory of the FIR-filters. w(n-1) w(n) Current data register Convolution processor: Register of constants

  10. 0 Types of FIR – filters 3. Band-pass filter (BPF) 2. High-pass filter (HPF) 1. Low-pass filter (LPF) 5. Differentiating filter 6. Integrating filter 4. Band-stop filter (BSF)

  11. Filter Specifications

  12. Symmetric form of the FIR – filter equation: (1) (2) (2a) (or even filter) Symmetric filter: (2b) (or odd filter) Skew – symmetric filter: For symmetric filter: (3) For skew-symmetric filter: (4)

  13. W(f) 1 Normally: f0=(0.15 : 0.25)fs f -f0 f0 f0 -fs fs -0.5fs 0.5fs Even filter: (5) Low-pass Filters (LPF) Odd filter: (6) Ideal LPF: (7) (8) (9)

  14. W(j) 2=s |W(j)|2 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 2=s =N s/2 

  15. N=51 >> b=0.25*sinc(0.25*(-25:25)); >> fvtool(b,1) N=501

  16. Logarithmic Scale N=51 N=501

  17. The Windowing Technique (10) (11) >> b=0.25*sinc(0.25*(-25:25)); >> b=b.*hamming(51); >> fvtool(b,1) Hamming window:

  18. Phase Response 0 -5 Phase (radians) -10 -15 -20 -25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 p Normalized Frequency ( ґ rad/sample) Linear Phase Response (12) W(z)=W(z-1)(12a) Group delay: (13)

  19. firpm firls %low-pass fir-filters design using different commands n = 20; % Filter order f = [0 0.4 0.5 1]; % Frequency band edges a = [1 1 0 0]; % Desired amplitudes b = firpm(n,f,a); % Design fir-filter using Parks -McClellan algorithm bb = firls(n,f,a); %Design fir-filter using leastsquare method fvtool(b,1,bb,1) % Filter Visualization FIR-filters Design Methods

  20. 0 a High –pass (hp) FIR-filters (a) Different FIR-filters Design All-pass (ap) filters: So: b High-pass filters: (14) Band –pass (bp) FIR-filters (b): (15) Band –stop (bs) FIR-filters (c): (16) c

  21. High-pass and Band-stop FIR-filters. %high-pass and bandstop filters n=20; fh = [0 0.7 0.8 1]; % Band edges in pairs ah = [0 0 1 1]; % Highpass filter amplitude fb = [0 0.3 0.4 0.5 0.8 1]; % Band edges in pairs ab = [1 1 0 0 1 1]; % Bandstop filter amplitude bh=firls(n,fh,ah); bs=firls(n,fb,ab); fvtool(bh,1,bs,1)

  22. %multiband fir-filter n=40; f = [0 0.1 0.15 0.25 0.3 0.4 0.45 0.55 0.6 0.7 0.75 0.85 0.9 1]; a = [1 1 0 0 1 1 0 0 1 1 0 0 1 1]; b= firls(n,f,a); fvtool(b,1) Multiband FIR-filter.

  23. n = 20; % Filter order f = [0 0.4 0.5 1]; % Frequency band edges a = [1 1 0 0]; % Desired amplitudes w = [1 10]; % Weight vector b = firpm(n,f,a,w); w1 = [1 2]; b1 = firpm(n,f,a,w1); fvtool(b,1,b1,1) Suppression of Ripples

  24. Differentiators (17) (18) Example: N=3. (19) (20) (21)

  25. bd b Design of Differentiators %differentiators b=firpm(20,[0 0.9],[0 0.9*pi],'d'); bd=firpm(21,[0 1],[0 pi],'d'); fvtool(b,1,bd,1)

  26. %low-pass fir-filters design using different commands n = 50; % Filter order f = [0 0.4 0.5 1]; % Frequency band edges a = [1 1 0 0]; % Desired amplitudes b = firls(n,f,a); [h,t]=stepz(b); [i,t]=impz(b); plot(t,h,'b',t,i,'m'), grid on Impulse and Step Responses

More Related