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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

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Pulse code modulation l.jpg
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)


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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)


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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


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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


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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


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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


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Discrete Cosine Transform (DCT)

  • DCT is the real part of the 2D Fourier transform

  • The inverse DCT is


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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


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DCT Basis Functions

  • The basis functions for a 8x8 DCT Transform


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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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