A companding operation compresses dynamic of input samples for encoding and expands dynamic range on decodeing. Optimal application of compading prodecude requires accurate estimation of pdf of input values from which non-linear x[n] transformation can be derived. In practice, however, such transformations are T standardized under CCITT international standard coder at 64 kbps; specifically A-law and companding. A-law is used in Europe while in North America. –law –law The -law transformation is given by: The -law transformation for 255, American PCM standard, is followed by 8-bit uniform quantization, 7-bits for value and 1-bit for sign, achieves quality of “toll speech” in telephone channels. Achieved toll quality is equivalent quality to straight uniform quantization using 12 bits. Due to standardization, in digital telephone networks and voice modems, standard CODEC chips are used in which audio is digitized in a 8-bit format. Figure . Block diagram of companding in the transmitting and receiving DSP system. is unquanitzed input sample with a nonuniform pdf of values, is x[n] y[n] the value obtained after nonlinear transformation with uniform pdf values, is quantized sample, is encoded binary representation of this sample c[n] value. This binary encoded stream is typically transmitted to a receiving system where it is converted back to original by decoding the input encoded samples , and applying inverse of the non-linear transformation to T-1 c’[n] obtaining sequence If differs from by = x’[n]. c’[n] c[n], x’[n] x[n] amount of introduced quantization noise. Data Representations The DSP’s, similarly to general computer processors, support a number of data formats. The variety of data formats and computational operations determine DSP capabilities. Most general classification of DSP processors is in terms of their hardware support of data types for various operations (e.g., addition, subtraction, multiplication and division). DSP’s are thus categorized as fixed-point or floating-point devices. Fixed-point data are computer representations of integer numbers. Floating-point data types are computer representations of real numbers.
A companding operation compresses dynamic of input samples for encoding and expands dynamic range on decodeing. Optimal application of compading prodecude requires accurate estimation of pdf of input x[n] values from which non-linear transformation T can be derived. In practice, however, such transformations are standardized under CCITT international standard coder at 64 kbps; specifically A-law and –law companding. A-law is used in Europe while –law in North America. The -law transformation is given by: The -law transformation for 255, American PCM standard, is followed by 8-bit uniform quantization, 7-bits for value and 1-bit for sign, achieves “toll quality of speech” in telephone channels. Achieved toll quality is equivalent quality to straight uniform quantization using 12 bits. Due to standardization, in digital telephone networks and voice modems, standard CODEC chips are used in which audio is digitized in a 8-bit format. Figure . Block diagram of companding in the transmitting and receiving DSP system. x[n] is unquanitzed input sample with a nonuniform pdf of values, y[n] is the value obtained after nonlinear transformation with uniform pdf values, is quantized sample, c[n] is encoded binary representation of this sample value. This binary encoded stream is typically transmitted to a receiving system where it is converted back to original by decoding the input encoded samples c’[n] to , and applying inverse of the non-linear transformation T-1 obtaining sequence x’[n]. If c’[n] = c[n], x’[n] differs from x[n] by amount of introduced quantization noise. Data Representations The DSP’s, similarly to general computer processors, support a number of data formats. The variety of data formats and computational operations determine DSP capabilities. Most general classification of DSP processors is in terms of their hardware support of data types for various operations (e.g., addition, subtraction, multiplication and division). DSP’s are thus categorized as fixed-point or floating-point devices. Fixed-point data are computer representations of integer numbers. Floating-point data types are computer representations of real numbers.
DSP%20from%20Theory%20to%20Practical%20Audio%20and%20Video%20Applications.docx