Digital Coding of Waveforms

You must turn in your code as well as output files. Please generate a report that contains the code and ouput in a single readable format. Getting Started  You may want to download Irfanview image viewing software. It handles pretty much any image type, lets you convert, and provides batch processing.  Download the sample images from the class website. The following question operates on the city.jpg image. (a) Perform image smoothing using a 7×7 averaging filter and a Gaussian filter with σ = 0.5 and 3. Compare the outputs. (b) Perform edge enhancement using the Sobel operator (Matlab's default parameters). Repeat using the Laplacian and Laplacian of Guassian operators. Compare the outputs 2. Frequency Domain Filtering The following question operates on the city.jpg image. (a) Find the Fourier transform of the image. Be sure to center the frequencies. (b) Perform image smoothing in the frequency domain using the filters defined in the previous problem. Compare the output images from the two methods (spatial and frequency) and the time for operation. (c) Perform edge enhancement using the filters defined in the previous problem. (d) Define a lowpass filter in the frequency domain with radius of 1/4 the height. Show the result. Repeat with a similar sized Guassian and compare the results. Give the σ parameter you used and show the output transform image. (e) Repeat with a rectangular filter with the same dimension as the ideal lowpass. Compare the results between the ideal filter and the rectangular approximation. 3. Canny Edge Detection (a) Give the convolution kernels for determining the gradient. You may examine the function gradient.m to help with the explanation. (It may be easiest to apply the gradient to an impulse and inspect the results. (b) Implement the simplified version of the Canny edge detector (single scale). The syntax of the function should be where E contains the detected edges, M the smoothed gradient magnitude, A contains the gradient angle, I is the input image, sig is the σ parameter for the smoothing filter, and tau= [τ h , τ l ] is the two element vector containing the hysteresis thresholds. See Algorithm 6.4 for non-maximal suppression and Algorithm 6.5 for hysteresis thresh-olding. (It may be more efficient to implement the hysteresis as edge tracking)

http://ieeexplore.ieee.org/iel5/5/31355/01457626.pdf

Multidimensional digital signal processing

A video coding method progressively refines a predicted motion vector to obtain an estimated motion vector. Subsequent steps are omitted if the estimated motion vector matches a current macroblock. Variable matching thresholds can permit dynamic adjustment of image quality and computational cost to optimize encoding performance for available computational resources. The method permits control of desired encoding speed and bit rate by adjusting encoding parameters. Video coders according to the invention may comprise a motion estimator, transform computer and coder each of which operates according to one or more parameters. A speed rate control and/or a bit rate control may adjust the parameters to maintain a desired encoding speed and output bit rate. A coder according to the invention may be implemented in software running on a general purpose computer. The method may be used in block-based video encoders including MPEG-2 and H.263 encoders.

Method and apparatus for video coding

It is well known that if each coefficient value of a digital filter is a sum of signed power-of-two (SPT) terms, the filter can be implemented without using multipliers. In the past decade, several methods have been developed for the design of filters whose coefficient values are sums of SPT terms. Most of these methods are for the design of filters where all the coefficient values have the same number of SPT terms. It has also been demonstrated recently that significant advantage can be achieved if the coefficient values are allocated with different number of SPT terms while keeping the total number of SPT terms for the filter fixed. In this paper, we present a new method for allocating the number of SPT terms to each coefficient value. In our method, the number of SPT terms allocated to a coefficient is determined by the statistical quantization step-size of that coefficient and the sensitivity of the frequency response of the filter to that coefficient. After the assignment of the SPT terms, an integer-programming algorithm is used to optimize the coefficient values. Our technique yields excellent results but does not guarantee optimum assignment of SPT terms. Nevertheless, for any particular assignment of SPT terms, the result obtained is optimum with respect to that assignment.

Signed Power-of-Two Term Allocation Scheme for the Design of Digital Filters

Techniques and tools for high accuracy position calculation for picture resizing in applications such as spatially-scalable video coding and decoding are described. In one aspect, resampling of a video picture is performed according to a resampling scale factor. The resampling comprises computation of a sample value at a position i, j in a resampled array. The computation includes computing a derived horizontal or vertical sub-sample position x or y in a manner that involves approximating a value in part by multiplying a 2n value by an inverse (approximate or exact) of the upsampling scale factor. The approximating can be a rounding or some other kind of approximating, such as a ceiling or floor function that approximates to a nearby integer. The sample value is interpolated using a filter.

Resampling and picture resizing operations for multi-resolution video coding and decoding

A Motion Compensation Technique for Down-Scaled Pictures in Layered Coding

In this paper a new lossless coding of digital image data with a four channel filter bank (4ch FB) having optimized filter coefficients is proposed The method has an advantage of less restrictions on optimizing the filter coefficients compared to the cascade form of two channel filter banks (2ch FB) Simulation results are shown to confirm its effectiveness

Lossless coding of still images with four channel prediction

A Realization of Active Current-Mode Resonator with Complex Coefficients Using CCIIs

In this paper, two universal building blocks for complex filter using CCIIs, CFCCIIs, grounded resistors and grounded capacitors are presented. These can be used to realize various complex bandpass filters with arbitrary order. The paper shows that the response error of the proposed circuit caused by nonideality of active components is more easily compensated than that of the conventional one employing op-amps, and that the sensitivities for all components are relatively small. Experimental results are used for verifying the validity of the proposed circuits.

Realization of Universal Active Complex Filter Using CCIIs and CFCCIIs

In this paper, we propose a bit-rate adaptive coding system based on lossless DCT (L-DCT). Our adaptive coding system consists of three different operation modes: lossless, near-lossless and lossy coding modes. Quantization is applied in transform domain (after the LDCT) and spatial domain (before the L-DCT) in lossy mode and near-lossless mode, respectively. Our adaptive coding system can automatically select its operation mode at a given bit rate because it contains a function to calculate the turning point between near-lossless mode and lossy mode from characteristic of input signal. Existence of the turning point is mathematically proved in this paper. Simulation results confirm not only effectiveness of our adaptive coding system but also accuracy of our theoretical analysis. key words: lossless DCT (L-DCT), coding, lossy, lossless, nearlossless, adaptive

Noriyoshi Kambayashi

Papers

A Motion Compensation Technique for Down-Scaled Pictures in Layered Coding

Lossless coding of still images with four channel prediction

A Realization of Active Current-Mode Resonator with Complex Coefficients Using CCIIs

Realization of Universal Active Complex Filter Using CCIIs and CFCCIIs

A Bit-Rate Adaptive Coding System Based on Lossless DCT