After studying this chapter you will be able to understand: Frequency spectrum of an image, explain the sampling of the 2 dimension image, the second stage of the digitization process, in the first sampling and in the second quantization of each of the samples, optimum mean square error or lloyd-max quantizer, designing of an optimum quantizer with the given signal probability density function. | Digital Image Processing Digitization Summery of previous lecture Need for the digitization To digitize the image Sampling Quantization How to digitize an image? Sampling of 1 dimensional signal f (t) We learn to use the Fourier transform to find out the bandwidth or the frequency spectrum of 1 dimensional signal f (t) if its periodic signal and if f (t) is an aperiodic signal Todays lecture Frequency spectrum of an image Explain the sampling of the 2 dimension image The second stage of the digitization process. In the first sampling and in the second quantization of each of the samples. Optimum mean square error or Lloyd-max quantizer. Designing of an optimum quantizer with the given signal probability density function. Theory of sampling Sampling from signal The sampling will be proper if its to be reconstruct the original continuous signal X (t) from these sampled values For that needs to maintain certain conditions so that the reconstruction of the analog signal X (t) is possible. Convolution Theorem if we have 2 signals X (t) and y (t) in time domain, then the multiplication of X (t) and y (t) in time domain is equivalent to the convolution of the frequency spectrum of X (t) and frequency spectrum of y (t) in the frequency domain, that is X (t) into y (t) is equivalent to X omega convoluted with Y omega. X omega is the frequency spectrum or the bandwidth of the signal, a frequency spectrum of the signal which is presented here and this is the frequency spectrum of the sampling function; these 2 are convolute, where the original frequency spectrum of the signal gets replicated along the frequency axis at an interval of 1 upon delta tS where 1 upon delta tS is nothing but the sampling frequency f of s. For proper reconstruction, we the original spectrum, And to take the original spectrum we need to take it out with a filter a particular band and the remaining frequency components will simply be discarded. For the filtering operation to be successful, we need 1 . | Digital Image Processing Digitization Summery of previous lecture Need for the digitization To digitize the image Sampling Quantization How to digitize an image? Sampling of 1 dimensional signal f (t) We learn to use the Fourier transform to find out the bandwidth or the frequency spectrum of 1 dimensional signal f (t) if its periodic signal and if f (t) is an aperiodic signal Todays lecture Frequency spectrum of an image Explain the sampling of the 2 dimension image The second stage of the digitization process. In the first sampling and in the second quantization of each of the samples. Optimum mean square error or Lloyd-max quantizer. Designing of an optimum quantizer with the given signal probability density function. Theory of sampling Sampling from signal The sampling will be proper if its to be reconstruct the original continuous signal X (t) from these sampled values For that needs to maintain certain conditions so that the reconstruction of the analog signal X (t) is possible.
