discrete cosine transform presentation.pptx

For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose. For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose.For an M-by-M matrix A , T*A is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of A . The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real

1. Speech Compression Using DCT

2. ABSTRACT Speech compression is a fundamental aspect of modern communication systems and enabling efficient transmission and storage of audio data. Discrete Cosine Transform (DCT) has emerged as a powerful tool in speech compression due to its ability to concentrate signal energy into a reduced set of coefficients. This paper presents analysis of speech compression using DCT, focusing on the mathematical underpinnings and practical implementation aspects. The trade-off between compression ratio and quality is carefully examined, considering parameters such as thresholding and quantization step size.

3. ABSTRACT Evaluation metrics including Signal-to-Noise Ratio (SNR) and Mean Squared Error (MSE) are utilized to assess the fidelity of the reconstructed speech signal. Through mathematical analysis and experimental validation, this study highlights the efficacy of DCT-based speech compression in achieving significant compression ratios while preserving perceptual quality. The findings contribute to the understanding and optimization of speech compression techniques, paving the way for enhanced audio communication systems in various domains.

4. INTRODUCTION Objective of speech is communication , whether face to face or cell phone to cell phone. A huge amount of data is a big issue for transmission or storage . Speech compression is the technology of converting human speech into an efficiently encoded representation that can later be decoded to produce a close approximation of the original signal. Major objective of speech compression is to represent speech with less or few numbers of bits with level of quality.

5. INTRODUCTION By removing redundancy between neighboring samples signal can be compressed. In this paper we have implemented compression technique in two steps, in 1st step a transform function is applied on speech signal to get result with a new set of data with smaller values and more repetition, 2nd step is coding(compression) step, this step will represent the data set in its minimal form by using encoding techniques such as Run Length encoding, Huffman encoding, run length encoding followed by Huffman encoding. Performance measures compression factor (CF), signal to noise ratio (SNR), peak signal to noise ratio (PSNR), normalized root mean square error (NRMSE), retained signal energy (RSE) is measured for reconstructed speech obtained DCT based speech compression techniques.

6. Objectives Here are four specific objectives of speech compression using DCT: Enhancing data storage efficiency by reducing the size of speech signals Minimizing bandwidth requirements for speech transmission Mitigating storage and transmission costs Preserving essential speech features while reducing redundancy enabling efficient utilization of communication resources in various applications.

7. Statement of the Problem: Speech compression is a critical aspect of various applications including telecommunications, multimedia streaming, and storage systems . Efficient compression techniques are essential to reduce the storage requirements and bandwidth usage while maintaining acceptable audio quality . In this context, the utilization of the Discrete Cosine Transform (DCT) for speech compression presents a promising approach.

8. SYSTEM DESIGN AND MATHEMATICAL ANALYSIS Methodology for compression of speech signal In this paper we are implementing speech compression technique based on DCT transform method. in case of DCT transform speech can be represented in terms of DCT coefficient . Thus, data operation can be performed using just the corresponding DCT coefficients. Transform techniques and thresholding does not actually compress a signal, it simply provides information about the signal , which allows the data to be compressed by standard encoding techniques. Speech compression is achieved by neglecting small coefficients as insignificant data and discarding them and then applying quantization and encoding scheme on coefficients.

9. SYSTEM DESIGN Methodology for compression of speech signal Steps in Speech Compression using DCT: Segmentation : Divide the speech signal into small segments or frames. Each frame typically consists of a few milliseconds of audio data. DCT Transformation : Apply DCT to each frame of the speech signal. Quantization : Quantize the DCT coefficients by rounding them to a smaller number of bits or by using a quantization matrix. This step reduces the precision of the coefficients. Entropy Coding : Apply entropy coding techniques (e.g., Huffman coding) to further compress the quantized coefficients. Transmission/Storage : Transmit or store the compressed coefficients along with necessary side information (e.g., frame size, quantization parameters) to reconstruct the speech signal. Reconstruction : At the decoder side, inverse the compression process by applying the inverse steps: entropy decoding, dequantization, inverse DCT, and frame concatenation.

10. System Block Diagram .

11. MATHEMATICAL ANALYSIS Mathematical model

12. METHODOLOGY Mathematical model

13. RESULT AND DISCUSSION Performance evaluation To evaluate the overall performance of the proposed audio compression scheme, several objective tests were made. To measure the performance of the reconstructed signal, various factors such as compression factor, Signal to noise ratio, PSNR& mean square error are taken into consideration.

14. RESULT AND DISCUSSION Performance evaluation Signal to Noise Ratio (SNR) Where σx 2 is the mean square of the speech signal and σe 2 is the mean square difference between the original and reconstructed speech signal.

15. RESULT AND DISCUSSION Performance evaluation Peak Signal to Noise Ratio (PSNR) Where N is the length of reconstructed signal, X is the maximum absolute square value of signal x and ||x-x`|| 2 is the energy of the difference between the original and reconstructed signal.

16. RESULT AND DISCUSSION Performance evaluation Normalized Root Mean Square Error (NRMSE ) Here, X(n) is the speech signal, x‟(n) is reconstructed speech signal and μ x(n) is the mean of speech signal.

17. RESULT AND DISCUSSION Results The results for Compression factor, Signal to Noise ratio, PSNR & Mean square error for the speech signal using the DCT based compression are summarized in table 1. No Error PSNR RMSE Size before compression Size after Decompression 1 3.0587e+04 21.8790 174.8914 110033 110033

18. RESULT AND DISCUSSION Results

19. CONCLUSION In conclusion, speech signal compression can be achieved through various methods, but one of the simplest and effective approaches is employing the Discrete Cosine Transform (DCT). By applying DCT, we can identify threshold coefficients within the speech signal and subsequently reduce its size, thereby facilitating efficient compression.

20. CONCLUSION While numerous other transforms and techniques exist for speech signal compression, the utilization of DCT stands out as the simplest and widely adopted method. Its effectiveness lies in its ability to efficiently represent the signal in the frequency domain, enabling significant reductions in data size while preserving essential information within the speech signal.

21. Thank you