Introduction to Filters under labVIEW Environment
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The document is a practical report on designing various finite impulse response (FIR) filters using LabVIEW, covering low pass and band pass filters with specific parameters. It includes detailed steps for calculating filter coefficients, applying window functions, and provides a list of available filter icons in LabVIEW for digital signal processing. Additionally, it discusses different types of filters and commonly used window functions in filter design.
![1. Design a Finite Impulse Response Low Pass Filter using rectangular window with a cut off
3 | P a g e
frequency of 1 KHz and sampling rate of 4 KHz with 11 samples.
1 −휔푐 ≤ 휔 ≤ 휔푐
0 −
휔푐
LabVIEW
Given:
Fs : 4 KHz
fc : 1 KHz
N : 11
Step: 1 - Finding Hd(ωt):
퐻푑 (휔푇) =
[
휔푠
2
≤ 휔 ≤ −휔푐
0 휔푐 ≤ 휔 ≤
휔푠
2 ]
휔푠 = 2휋푓푠 = 25132.74 푟푎푑/푠푒푐
푇 =
1
푓푠
= 0.25 ∗ 10−3푠푒푐
Step: 2 – Finding hd(n):
ℎ푑 (푛) =
1
휔푠
∫ 푒푗휔푛푇 . 푑휔
−휔푐
ℎ푑 (푛) =
2
휔푠 푛푇
∗ 푆푖푛(휔푐 푛푇)
ℎ푑 (푛) =
푆푖푛(휔푐 푛푇)
휋푛
; 푤ℎ푒푛 푛 ≠ 0
ℎ푑 (푛) =
2휔푐
휔푠
; 푤ℎ푒푛 푛 = 0
Step: 3 – Window Function:
휔푟 (푛) = [
1 푓표푟 푛 = 0 푡표 푀 − 1
0 표푡ℎ푒푟푤푖푠푒
]
Step: 4 – Coefficients:
hd(n) 0.5 0.3183 0 -0.1061 0 0.0637 -0.0455 0 0.0354 0
ωr(n) 1 1 1 1 1 1 1 1 1 1
h(n) 0.5 0.3183 0 -0.1061 0 0.0637 -0.0455 0 0.0354 0](https://image.slidesharecdn.com/introductiontofiltersunderlabviewenvironment-141211073724-conversion-gate01/85/Introduction-to-Filters-under-labVIEW-Environment-3-320.jpg)
![2. Design a Finite Impulse Response Band Pass Filter using Triangular (Bartlett) window with a
lower cut off frequency of 3 KHz, higher cut off frequency of 5.5 KHz and sampling rate of 20
KHz with 15 samples (Order-14).
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푆푖푛(휔푐1(푛 − 푀))
LabVIEW
Given:
Fs : 20 KHz
fcl : 3 KHz
fch : 5.5 KHz
N : 15
Step: 1 – Finding hd(n):
ℎ푑 (푛) = [
휋 (푛 − 푀)
−
푆푖푛(휔푐2(푛 − 푀))
휋(푛 − 푀)
푛 ≠ 푀
1 −
휔푐2−휔푐1
휋
푛 = 푀
]
Where: M index of middle coefficient.
휔푐1 =
2휋푓푐1
푓푠
= 0.3휋
휔푐2 =
2휋푓푐2
푓푠
= 0.55휋
Step: 2 – Window Function:
휔[푛] = [
2푛
푁 − 1
; 푓표푟 0 ≤ 푛 ≤ 푡표
푁 − 1
2
2 −
2푛
푁 − 1
;
푁 + 1
2
≤ 푛 ≤ 푁 − 1
]
Step: 3 – Coefficients:
Coefficient 0 1 2 3 4 5 6 7
hd(n) 0.034696 0.011737 -0.10868 -0.09355 0.127326 0.200547 -0.05687 0.75
ωr(n) 0 0.142857 0.285714 0.428571 0.571429 0.714286 0.857143 1
h(n) 0 0.001677 -0.03105 -0.04009 0.072758 0.143248 -0.048747 0.75
Coefficient 8 9 10 11 12 13 14
hd(n) 0.056872 -0.20055 -0.12733 0.093549 0.108678 -0.01174 -0.034696
ωr(n) 0.857143 0.714286 0.571429 0.428571 0.285714 0.142857 0
h(n) -0.048747 0.143248 0.072758 -0.040092 -0.031051 0.001667 0](https://image.slidesharecdn.com/introductiontofiltersunderlabviewenvironment-141211073724-conversion-gate01/85/Introduction-to-Filters-under-labVIEW-Environment-5-320.jpg)
![7 | P a g e
3. Type of filter and commonly used Windows.
S.No. Type of Filter Frequency Response hd[n]
푆푖푛(휔푐 (푛 − 푀))
1. Low Pass Filter ℎ푑 (푛) = [
0.54 + 0.46 ∗ 퐶표푠
LabVIEW
휋(푛 − 푀)
푛 ≠ 푀
휔푐
휋
푛 = 푀
]
2. High Pass Filter ℎ푑 (푛) = [
1 −
휔푐
휋
푛 ≠ 푀
−
푆푖푛(휔푐 (푛 − 푀))
휋(푛 − 푀)
푛 = 푀
]
3. Band Pass Filter ℎ푑 (푛) = [
푆푖푛(휔푐2(푛 − 푀))
휋(푛 − 푀)
−
푆푖푛(휔푐1(푛 − 푀))
휋(푛 − 푀)
푛 ≠ 푀
휔푐2− 휔푐1
휋
푛 = 푀
]
4. Band Stop Filter ℎ푑 (푛) = [
푆푖푛(휔푐1(푛 − 푀))
휋(푛 − 푀)
−
푆푖푛(휔푐2(푛 − 푀))
휋(푛 − 푀)
푛 ≠ 푀
1 −
휔푐2− 휔푐1
휋
푛 = 푀
]
S. No. Window Function
1. Triangular (Bartlett) 푊푇 [푛] =
2|푛|
푀 − 1
; 푓표푟 |푛| ≤ 푀 − 1
2. Hanning 푊ℎ푛 =
1
2
[1 −
퐶표푠2휋푛
푀 − 1
] ;
3. Hamming 푊퐻푚 = [
2휋푛
푀 − 1
; |푛| ≤ 푄
0; 푒푙푒푠푤ℎ푒푟푒
]
4. Blackman 푊퐵 [푛] = 0.42 + 0.5 ∗ 퐶표푠
2휋푛
푀 − 1
+ 0.08 ∗ 퐶표푠
4휋푛
푀 − 1
5. Kaiser 푊푘 [푛] = [
퐼표(훽)
퐼표(훼)
|푛| ≤ 푄
0; 푒푙푒푠푤ℎ푒푟푒
]](https://image.slidesharecdn.com/introductiontofiltersunderlabviewenvironment-141211073724-conversion-gate01/85/Introduction-to-Filters-under-labVIEW-Environment-7-320.jpg)
Introduction to Filters under labVIEW Environment
- 1. 1 | P a g e A Practical Report on INTRODUCTION TO FILTERS Under LabVIEW Environment Submitted To: Submitted By: Mr. Raj Kumar Garg Paramjeet Singh Jamwal Assistant Professor PG/ICE/136321 LabVIEW M.Tech (ICE) Third Semester Department of Electrical and Instrumentation Engineering Sant Longowal Institute of Engineering and Technology Longowal – 148106 (INDIA) Nov 2014
- 2. 2 | P a g e CONTENT S. No. Example Page No. 1. Design a Finite Impulse Response Low Pass Filter using rectangular window with a cut off frequency of 1 KHz and sampling rate of 4 KHz with 11 samples. LabVIEW 3. 2. Design a Finite Impulse Response Band Pass Filter using Triangular (Bartlett) window with a lower cut off frequency of 3 KHz, higher cut off frequency of 5.5 KHz and sampling rate of 20 KHz with 15 samples (Order-14). 5. 3. Type of filter and commonly used Windows. 7. 4. List of filter icon available in the LabVIEW. 8.
- 3. 1. Design a Finite Impulse Response Low Pass Filter using rectangular window with a cut off 3 | P a g e frequency of 1 KHz and sampling rate of 4 KHz with 11 samples. 1 −휔푐 ≤ 휔 ≤ 휔푐 0 − 휔푐 LabVIEW Given: Fs : 4 KHz fc : 1 KHz N : 11 Step: 1 - Finding Hd(ωt): 퐻푑 (휔푇) = [ 휔푠 2 ≤ 휔 ≤ −휔푐 0 휔푐 ≤ 휔 ≤ 휔푠 2 ] 휔푠 = 2휋푓푠 = 25132.74 푟푎푑/푠푒푐 푇 = 1 푓푠 = 0.25 ∗ 10−3푠푒푐 Step: 2 – Finding hd(n): ℎ푑 (푛) = 1 휔푠 ∫ 푒푗휔푛푇 . 푑휔 −휔푐 ℎ푑 (푛) = 2 휔푠 푛푇 ∗ 푆푖푛(휔푐 푛푇) ℎ푑 (푛) = 푆푖푛(휔푐 푛푇) 휋푛 ; 푤ℎ푒푛 푛 ≠ 0 ℎ푑 (푛) = 2휔푐 휔푠 ; 푤ℎ푒푛 푛 = 0 Step: 3 – Window Function: 휔푟 (푛) = [ 1 푓표푟 푛 = 0 푡표 푀 − 1 0 표푡ℎ푒푟푤푖푠푒 ] Step: 4 – Coefficients: hd(n) 0.5 0.3183 0 -0.1061 0 0.0637 -0.0455 0 0.0354 0 ωr(n) 1 1 1 1 1 1 1 1 1 1 h(n) 0.5 0.3183 0 -0.1061 0 0.0637 -0.0455 0 0.0354 0
- 4. 4 | P a g e LabVIEW Step: 5.1 – Block Diagram: Step: 5.2 – Front Panel: Reference: Salivahnan S., Ghananpriya C., “Digital Signal Processing”, 2nd Edition, pp-439-440, Example-7.4.
- 5. 2. Design a Finite Impulse Response Band Pass Filter using Triangular (Bartlett) window with a lower cut off frequency of 3 KHz, higher cut off frequency of 5.5 KHz and sampling rate of 20 KHz with 15 samples (Order-14). 5 | P a g e 푆푖푛(휔푐1(푛 − 푀)) LabVIEW Given: Fs : 20 KHz fcl : 3 KHz fch : 5.5 KHz N : 15 Step: 1 – Finding hd(n): ℎ푑 (푛) = [ 휋 (푛 − 푀) − 푆푖푛(휔푐2(푛 − 푀)) 휋(푛 − 푀) 푛 ≠ 푀 1 − 휔푐2−휔푐1 휋 푛 = 푀 ] Where: M index of middle coefficient. 휔푐1 = 2휋푓푐1 푓푠 = 0.3휋 휔푐2 = 2휋푓푐2 푓푠 = 0.55휋 Step: 2 – Window Function: 휔[푛] = [ 2푛 푁 − 1 ; 푓표푟 0 ≤ 푛 ≤ 푡표 푁 − 1 2 2 − 2푛 푁 − 1 ; 푁 + 1 2 ≤ 푛 ≤ 푁 − 1 ] Step: 3 – Coefficients: Coefficient 0 1 2 3 4 5 6 7 hd(n) 0.034696 0.011737 -0.10868 -0.09355 0.127326 0.200547 -0.05687 0.75 ωr(n) 0 0.142857 0.285714 0.428571 0.571429 0.714286 0.857143 1 h(n) 0 0.001677 -0.03105 -0.04009 0.072758 0.143248 -0.048747 0.75 Coefficient 8 9 10 11 12 13 14 hd(n) 0.056872 -0.20055 -0.12733 0.093549 0.108678 -0.01174 -0.034696 ωr(n) 0.857143 0.714286 0.571429 0.428571 0.285714 0.142857 0 h(n) -0.048747 0.143248 0.072758 -0.040092 -0.031051 0.001667 0
- 6. 6 | P a g e LabVIEW Step: 4.1 – Block Diagram: Step: 4.2 – Front Panel: Reference: “Mikro Elektronika”, http://www.mikroe.com/chapters/view/72/chapter-2-fir-filters/.
- 7. 7 | P a g e 3. Type of filter and commonly used Windows. S.No. Type of Filter Frequency Response hd[n] 푆푖푛(휔푐 (푛 − 푀)) 1. Low Pass Filter ℎ푑 (푛) = [ 0.54 + 0.46 ∗ 퐶표푠 LabVIEW 휋(푛 − 푀) 푛 ≠ 푀 휔푐 휋 푛 = 푀 ] 2. High Pass Filter ℎ푑 (푛) = [ 1 − 휔푐 휋 푛 ≠ 푀 − 푆푖푛(휔푐 (푛 − 푀)) 휋(푛 − 푀) 푛 = 푀 ] 3. Band Pass Filter ℎ푑 (푛) = [ 푆푖푛(휔푐2(푛 − 푀)) 휋(푛 − 푀) − 푆푖푛(휔푐1(푛 − 푀)) 휋(푛 − 푀) 푛 ≠ 푀 휔푐2− 휔푐1 휋 푛 = 푀 ] 4. Band Stop Filter ℎ푑 (푛) = [ 푆푖푛(휔푐1(푛 − 푀)) 휋(푛 − 푀) − 푆푖푛(휔푐2(푛 − 푀)) 휋(푛 − 푀) 푛 ≠ 푀 1 − 휔푐2− 휔푐1 휋 푛 = 푀 ] S. No. Window Function 1. Triangular (Bartlett) 푊푇 [푛] = 2|푛| 푀 − 1 ; 푓표푟 |푛| ≤ 푀 − 1 2. Hanning 푊ℎ푛 = 1 2 [1 − 퐶표푠2휋푛 푀 − 1 ] ; 3. Hamming 푊퐻푚 = [ 2휋푛 푀 − 1 ; |푛| ≤ 푄 0; 푒푙푒푠푤ℎ푒푟푒 ] 4. Blackman 푊퐵 [푛] = 0.42 + 0.5 ∗ 퐶표푠 2휋푛 푀 − 1 + 0.08 ∗ 퐶표푠 4휋푛 푀 − 1 5. Kaiser 푊푘 [푛] = [ 퐼표(훽) 퐼표(훼) |푛| ≤ 푄 0; 푒푙푒푠푤ℎ푒푟푒 ]
- 8. 8 | P a g e 4. List of filter icon available in the LabVIEW. Filter icon is available at Functions/Signal Processing/Filters. IIR Filter S. No. Icon Name Function LabVIEW 01. Butterworth Filter Generates a digital Butterworth filter by calling the Butterworth Coefficients VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 02. Chebyshev Filter Generates a digital Chebyshev filter by calling the Chebyshev Coefficients VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 03. Inverse Chebyshev Filter Generates a digital Chebyshev II filter by calling the Inv Chebyshev Coefficients VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 04. Elliptic Filter Generates a digital elliptic filter by calling the Elliptic Coefficients VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 05. Bessel Filter Generates a digital Bessel filter by calling the Bessel Coefficients VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 06. Butterworth Coefficients Generates the set of filter coefficients to implement an IIR filter as specified by the Butterworth filter model. You can pass these filter coefficients, IIR Filter Cluster, to the IIR Cascade Filter VI to filter a sequence of data. 07. Chebyshev Coefficients Generates the set of filter coefficients to implement an IIR filter as specified by the Chebyshev filter model. You can pass these coefficients to the IIR Cascade Filter VI to filter a sequence of data. 08. Inv Chebyshev Coefficients Generates the set of filter coefficients to implement an IIR filter as specified by the Chebyshev II Filter model. You can pass these coefficients to the IIR Cascade Filter VI to filter a sequence of data. 09. Elliptic Coefficients Generates the set of filter coefficients to implement a digital elliptic IIR filter. You can pass these coefficients to the IIR Cascade Filter VI. 10. Bessel Coefficients Generates the set of filter coefficients to implement an IIR filter as specified by the Bessel filter model. You then can pass these coefficients to the IIR Cascade Filter VI.
- 9. 9 | P a g e LabVIEW 11. Butterworth Order Estimation Estimates the Butterworth filter order. S. No. Icon Name Function 12. Chebyshev Order Estimation Estimates the Chebyshev I filter order. 13. Inverse Chebyshev Order Estimation Estimates the Inverse Chebyshev filter order. 14. Elliptic Order Estimation Estimates the Elliptic filter order. 15. Inverse f Filter Designs and implements an IIR filter whose magnitude-squared response is inversely proportional to frequency over a specified frequency range. This inverse-f filter is typically used to colorize spectrally flat, or white, noise. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 16. Inverse f Filter Coefficients Designs an IIR filter whose magnitude-squared response is inversely proportional to frequency over a specified frequency range. This inverse-f filter is typically used to colorize spectrally flat, or white, noise. 17. IIR Cascade Filter Filters the input sequence X using the cascade form of the IIR filter specified by the IIR Filter Cluster. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 18. IIR Cascade Filter with I.C. Filters the input sequence X using the cascade form of the IIR filter specified by the IIR Filter Cluster. This VI is similar to the IIR Cascade Filter VI except that you specify the initial conditions for this VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 19. IIR Filter Filters the input sequence X using the direct form IIR filter specified by Reverse Coefficients and Forward Coefficients. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 20. IIR Filter with I.C. Filters the input sequence X using the direct form IIR filter specified by Reverse Coefficients and Forward Coefficients. You can use this VI to process blocks of continuous data. This VI is similar to the IIR Filter VI except that you specify the initial conditions for this VI. Wire data to the X input to determine the polymorphic instance to use or manually select the instance.
- 10. 10 | P a g e LabVIEW 21. Cascade To Direct Coefficients Converts IIR filter coefficients from the cascade form to the direct form. FIR Filter S. No. Icon Name Function 22. Equi-Ripple LowPass Generates a lowpass FIR filter with equi-ripple characteristics using the Parks-McClellan algorithm and the # of taps, pass freq, stop freq, and sampling freq: fs. The Equi-Ripple LowPass VI then applies a linear-phase, lowpass filter to the input sequence X using the Convolution VI to obtain Filtered X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 23. Equi-Ripple HighPass Generates a highpass FIR filter with equi-ripple characteristics using the Parks-McClellan algorithm and the # of taps, stop freq, high freq, and sampling freq: fs. The Equi-Ripple HighPass VI then applies a linear-phase, highpass filter to the input sequence X using the Convolution VI to obtain Filtered X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 24. Equi-Ripple BandPass Generates a bandpass FIR filter with equi-ripple characteristics using the Parks-McClellan algorithm and the higher pass freq, lower pass freq, # of taps, lower stop freq, higher stop freq, and sampling freq: fs. The Equi- Ripple BandPass VI then applies a linear-phase, bandpass filter to the input sequence X using the Convolution VI to obtain Filtered X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 25. Equi-Ripple BandStop Generates a bandstop FIR digital filter with equi-ripple characteristics using the Parks-McClellan algorithm and higher pass freq, lower pass freq, # of taps, lower stop freq, higher stop freq, and sampling freq: fs. The Equi-Ripple BandStop VI then applies a linear-phase, bandstop filter to the input sequence X using the Convolution VI to obtain Filtered X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 26. FIR Windowed Filter Filters the input data sequence, X, using the set of windowed FIR filter coefficients specified by the sampling freq: fs, low cutoff freq: fl, high cutoff freq: fh, and number of taps. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 27. Savitzky-Golay Filter Filters the input data sequence X using a Savitzky-Golay FIR smoothing filter. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 28. FIR Windowed Coefficients Generates the set of filter coefficients you need to implement an FIR windowed filter.
- 11. 11 | P a g e LabVIEW 29. Parks-McClellan Generates a set of linear-phase FIR multiband digital filter coefficients using the # of taps, sampling frequency: fs, Band Parameters, and filter type. S. No. Icon Name Function 30. Savitzky-Golay Filter Coefficients Designs a Savitzky-Golay FIR smoothing filter. This VI returns the designed Savitzky-Golay filter coefficients and the differentiation filter coefficients. 31. FIR Narrowband Coefficients Generates a set of filter coefficients to implement a digital interpolated FIR (IFIR) filter. 32. FIR Filter Filters the input sequence X using the direct-form FIR filter specified by FIR Coefficients. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 33. FIR Filter with I.C. Filters the input sequence X using the direct-form FIR filter specified by FIR Coefficients. You can use this VI to process blocks of continuous data. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 34. FIR Narrowband Filter Filters the input sequence X using the interpolated FIR (IFIR) filter specified by IFIR Coefficients. Other Filter 35. Smoothing Filter Coefficients Designs filter coefficients for a smoothing filter. You can use this VI to design a moving-average FIR filter or an exponentially-averaging IIR filter. The VI returns reverse coefficients and forward coefficients for direct connection to the IIR Filter VI, which is used to implement both FIR and IIR filters. 36. Zero Phase Filter Applies a zero phase filter to an input sequence X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance. 37. Median Filter Applies a median filter of rank to the input sequence X, where rank is right rank if right rank is greater than zero, or left rank if right rank is less than zero. 38. Mathematical Morphological Filter Filters the input data sequence X with Structure Element using a mathematical morphological filter. 39. Convolution Computes the convolution of the input sequences X and Y. Wire data to the X and Y inputs to determine the polymorphic instance to use or manually select the instance. --- An info4eee presentation, which provides Information for Electrical and Electronics Engineering students. It is the initiative to share the material among the EEE students in a well mannered way. Now available on: info4eee.wordpress.com facebook.com/info4eee