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## PowerPoint Slideshow about 'Data Compression 2' - MartaAdara

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### Data Compression (2)

Hai Tao

Pulse code modulation

- The process of digitizing audio signal is called pulse code modulation
- Sampling the analog waveform at a minimum rate
- Each sample is quantized using a fixed number of bits

- To reduce the amount of data, we can
- Reduce the sampling rate (e.g 8k for telephone )
- Reduce the number of bit per sample (8 bits vs. 16 bits)

Differential Pulse Code Modulation (DPCM)

- Encode the changes between consecutive samples
- Example
- The value of the differences between samples are much smaller than those of the original samples. Less bits are used to encode the signal (e.g. 7 bits instead of 8 bits)

DPCM decoding

- The difference is added to the previous sample to obtain the value of the current sample. Lossless coding is achieved
- In DPCM, the number of bits per sample needs to accommodate the largest value changes between samples, both in positive and negative direction. For an original sequence of 8bit PCM, to tolerate ¼ of changes in both direction, 7 bits are needed to code the differences

Adaptive DPCM (ADPCM)

- One observation is that small difference between samples happens more often than large changes
- Entropy coding method such the Huffman coding scheme can be used to encode the difference for additional efficiency
- The probabilities of occurrence of different differences are first obtained using a large data base
- Huffman coding method is used to determine the codeword for each difference
- The codeword is fixed and made available to decoders

Linear Predictive Coding (LPC)

- In DPCM, the value of the current sample is guessed based on the previous sample. Can a better prediction be made ?
- The answer is yes. For example, we can use the previous two samples to predict the current one
- LPC is more general than DPCM. It exploit the correlation between multiple consecutive samples

Image Compression

- From the 1D case, we observe that data compression can be achieved by exploiting the correlation between samples. This idea is applicable to 2D signals as well.
- Instead of predicting sample values, we can use the so called transformation method to obtain a more compact representation of the data

Discrete Cosine Transform (DCT)

- DCT is the real part of the 2D Fourier transform
- The inverse DCT is

DCT Transform of 2D Images

- DCT Example
- DCT of images can also be considered as the projection of the original image into the DCT basis functions. Each basis function is in the form of

DCT Basis Functions

- The basis functions for a 8x8 DCT Transform

DCT Compression

- After DCT compression, only a few DCT coefficients have large values
- We need to
- Quantize the DCT coefficients
- Encode the position of the large coefficients
- Compress the value of the coefficients

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