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Digital Signal Processing

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Introduction

 

The main objective of this report is to make analysis on the image processing technique through discrete transform techniques. In this paper significant number of discrete transforms helps has been taken to analyse the image. Some of the used transforms technique in the image processing is discrete sine, discrete cosine, discrete Fourier transform and Walsh and Hadamard transforms.    

 

 

Part 1: Literature Review

 

Image analysis application has been found in the mobile communication devices like headsets, in normal communication services and in internet. In this case the discrete transforms has been used for specific process of image expansion which is named as interpolation and image size reduction. This study has undertaken through detail reviewing the algorithms using the transform techniques. FST and the DST are some of the best example taken to analyse the image processing.   

 

 

Image decimation:

In digital signalling process decimation process helps to reducing the signals and sampling rates. Decimation utilises the filtering in order to mitigate the aliasing distortion. This process can occur when the signal can get the down sampling. Decimator is a system component that performs the decimation. Decimation reduces size of the data and data rates.

The decimation factor used in the analysis is as integer or can be rational fraction which is greater than one. This factor divided the sampling rate and also multiplies the sampling time.    

Image interpolation:

In digital signal processing interpolation increases the sampling rate. Image interpolation is a specific case in multi rate digital signal processing system and used in sample rate conversion[1]. Interpolation in digital processing makes sampling through following the filtering techniques. Interpolation gives result in terms of sampling the signal at higher rate.

Interpolate factor can be derived from making ratio of output rate to input rate. This can be symbolised by ‘L’.

L= output rate/Input rate  

Discrete transform:

In digital processing system discrete transform is a mathematical linear transform. This is a produced signal between discrete frequency, discrete time and discrete domain.   

Fourier Transform:

This decomposes the function of time signals into the frequencies which makes up. It takes time based input and also determines the overall cycle offset.  

Analysis of Image decimation and interpolation using Discrete Transform:

Discrete cosine Transform:

DST represents any image in the form as a sum of sinusoids of varying frequencies and magnitude. The function of dct2 helps in computing the 2D DCT for an image. The DCT has often used for image compression applications as it considers few coefficients for analysis.

Walsh and Hadamard transforms

Two of the applications of Walsh and Hadamard transforms, has been used in digital processing are processing of ECG signals and communication using the spread spectrum. The WHTs has been used in filtering, medical signalling, power spectrum analysis, and coding, multiplexing, logical design and in analysis.

The WHT is a non sinusoidal, suboptimal and orthogonal transformation which decomposes rectangular waveforms. The Hadamard functions have two values namely +1 and -1. In this case also 8 Walsh functions has been generated and listed as below.

Part 3: Image interpolation code analysis

 

In case of image interpolation code analysis one of the Walsh-Transform applications has been considered. The Fast algorithm has been developed with complexity of O(NlogN). The derived matrix is of simplex in nature.

 

 

ECG signal processing:

The algorithm of the application can be represented as

The electrocardiograms signals can be noted at different instant of time are represented as below.

It has been observed that signal energy concentrated at very lower sequence of values. Higher frequency coefficients are suppressed. The signal rates are shown.

The reproduced signal rates in the WHT are very close to the original signals. The first 1024 coefficients and ECG signal lengths have been stored. The compression ratio delivered is of 4:1. 

Conclusion

 

In this report a brief analysis on the various discrete transform techniques has been done. Taking the WHT transform technique an example of ECG equipment algorithm implementation has been done. Cosine and Fourier transform analysis has been elaborated in brief manner.   

References


[1] Lilik, F., Nagy, S., & Kóczy, L. T. (2018). On Combination of Wavelet Transformation and Stabilized KH Interpolation for Fuzzy Inferences Based on High Dimensional Sampled Functions. In Interactions Between Computational Intelligence and Mathematics (pp. 31-42). Springer, Cham.

[2] Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications164(6).

Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications, 164(6).

[3] Lloyd, D. B., Boyd, C. N., & Govindaraju, N. K. (2016). U.S. Patent No. 9,342,486. Washington, DC: U.S. Patent and Trademark Office.

[4] Rawat, N., Kim, B., Muniraj, I., Situ, G., & Lee, B. G. (2015). Compressive sensing based robust multispectral double-image encryption. Applied Optics54(7), 1782-1793.

[5] Sudarshan, V. K., Mookiah, M. R. K., Acharya, U. R., Chandran, V., Molinari, F., Fujita, H., & Ng, K. H. (2016). Application of wavelet techniques for cancer diagnosis using ultrasound images: A Review. Computers in biology and medicine, 69, 97-111.

[6] Sudarshan, V. K., Mookiah, M. R. K., Acharya, U. R., Chandran, V., Molinari, F., Fujita, H., & Ng, K. H. (2016). Application of wavelet techniques for cancer diagnosis using ultrasound images: A Review. Computers in biology and medicine, 69, 97-111.

[7] Weniger, M., Kapp, F., & Friederichs, P. (2017). Spatial verification using wavelet transforms: a review. Quarterly Journal of the Royal Meteorological Society143(702), 120-136.

[8] Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications, 164(6).

[9] Sangeetha, S., & Kannan, P. (2017). Survey of Digital Filters for Speech Signals Using Multi-Rate Signal Processing. Imperial Journal of Interdisciplinary Research, 3(11).

[10] Weniger, M., Kapp, F., & Friederichs, P. (2017). Spatial verification using wavelet transforms: a review. Quarterly Journal of the Royal Meteorological Society, 143(702), 120-136.

[11] Rawat, N., Kim, B., Muniraj, I., Situ, G., & Lee, B. G. (2015). Compressive sensing based robust multispectral double-image encryption. Applied Optics, 54(7), 1782-1793.

[12] Lilik, F., Nagy, S., & Kóczy, L. T. (2018). On Combination of Wavelet Transformation and Stabilized KH Interpolation for Fuzzy Inferences Based on High Dimensional Sampled Functions. In Interactions Between Computational Intelligence and Mathematics (pp. 31-42). Springer, Cham.

[13] Lloyd, D. B., Boyd, C. N., & Govindaraju, N. K. (2016). U.S. Patent No. 9,342,486. Washington, DC: U.S. Patent and Trademark Office.

[14] Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications, 164(6).

[15] Gan, S., Wang, S., Chen, Y., Chen, X., Huang, W., & Chen, H. (2016). Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform. Journal of Applied Geophysics, 130, 194-208.

[16] Sangeetha, S., & Kannan, P. (2017). Survey of Digital Filters for Speech Signals Using Multi-Rate Signal Processing. Imperial Journal of Interdisciplinary Research3(11).

[17] Lloyd, D. B., Boyd, C. N., & Govindaraju, N. K. (2016). U.S. Patent No. 9,342,486. Washington, DC: U.S. Patent and Trademark Office.



[1] Lilik, F., Nagy, S., & Kóczy, L. T. (2018). On Combination of Wavelet Transformation and Stabilized KH Interpolation for Fuzzy Inferences Based on High Dimensional Sampled Functions. In Interactions Between Computational Intelligence and Mathematics (pp. 31-42). Springer, Cham.

[1] Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications164(6).

Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications, 164(6).

[1] Lloyd, D. B., Boyd, C. N., & Govindaraju, N. K. (2016). U.S. Patent No. 9,342,486. Washington, DC: U.S. Patent and Trademark Office.

[1] Rawat, N., Kim, B., Muniraj, I., Situ, G., & Lee, B. G. (2015). Compressive sensing based robust multispectral double-image encryption. Applied Optics54(7), 1782-1793.

[1] Sudarshan, V. K., Mookiah, M. R. K., Acharya, U. R., Chandran, V., Molinari, F., Fujita, H., & Ng, K. H. (2016). Application of wavelet techniques for cancer diagnosis using ultrasound images: A Review. Computers in biology and medicine, 69, 97-111.

[1] Sudarshan, V. K., Mookiah, M. R. K., Acharya, U. R., Chandran, V., Molinari, F., Fujita, H., & Ng, K. H. (2016). Application of wavelet techniques for cancer diagnosis using ultrasound images: A Review. Computers in biology and medicine, 69, 97-111.

[1] Weniger, M., Kapp, F., & Friederichs, P. (2017). Spatial verification using wavelet transforms: a review. Quarterly Journal of the Royal Meteorological Society143(702), 120-136.

[1] Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications, 164(6).

[1] Sangeetha, S., & Kannan, P. (2017). Survey of Digital Filters for Speech Signals Using Multi-Rate Signal Processing. Imperial Journal of Interdisciplinary Research, 3(11).

[1] Weniger, M., Kapp, F., & Friederichs, P. (2017). Spatial verification using wavelet transforms: a review. Quarterly Journal of the Royal Meteorological Society, 143(702), 120-136.

[1] Rawat, N., Kim, B., Muniraj, I., Situ, G., & Lee, B. G. (2015). Compressive sensing based robust multispectral double-image encryption. Applied Optics, 54(7), 1782-1793.

[1] Lilik, F., Nagy, S., & Kóczy, L. T. (2018). On Combination of Wavelet Transformation and Stabilized KH Interpolation for Fuzzy Inferences Based on High Dimensional Sampled Functions. In Interactions Between Computational Intelligence and Mathematics (pp. 31-42). Springer, Cham.

[1] Lloyd, D. B., Boyd, C. N., & Govindaraju, N. K. (2016). U.S. Patent No. 9,342,486. Washington, DC: U.S. Patent and Trademark Office.

[1] Karande, A. R., & Renke, A. L. (2017). A Review on Image Enhancement Methods. International Journal of Computer Applications, 164(6).

[1] Gan, S., Wang, S., Chen, Y., Chen, X., Huang, W., & Chen, H. (2016). Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform. Journal of Applied Geophysics, 130, 194-208.

[1] Sangeetha, S., & Kannan, P. (2017). Survey of Digital Filters for Speech Signals Using Multi-Rate Signal Processing. Imperial Journal of Interdisciplinary Research3(11).

[1] Lloyd, D. B., Boyd, C. N., & Govindaraju, N. K. (2016). U.S. Patent No. 9,342,486. Washington, DC: U.S. Patent and Trademark Office.

 

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