Transforms and Fast Algorithms for Signal Analysis and Representations

New fast algorithms for the low delay MDCT computation in the MPEG-4 AAC enhanced low delay audio coding standard

“…Many fast (recursive) algorithms/ computational structures for the efficient computation of the DCT-II and its inverse, DCT-III, are available in the literature both for 2 m -lengths [20,22,24,27,28] and composite lengths of the form 2 m  q, where q is the odd positive integer [30,31,33].…”

“…The efficient 15-point DCT-II module was derived in [30,31] by the prime factor decomposition (PFA) method, and it is shown in Fig. 1 ðInÞ 3n ¼ ðOutÞ n ; ðInÞ 3n þ 1 ¼ ðOutÞ 5 þ n ; ðInÞ 3n þ 2 ¼ ðOutÞ 10 þ n ; n ¼ 0; 1; 2; 3; 4:…”

Challenges of Implementing Cyber-Physical Security Solutions in Body Area Networks

“…This re-arrangement ensured that after the butterfly computation the output data elements can be stored in the same location as the input data elements; 2) Butterfly: The butterfly operation was performed on pairs of data elements that were fed serially into the butterfly. Butterfly operation consisted of two complex additions and two complex multiplications by the twiddle factor [3]; and 3) Storage: The results of the butterfly computation on the data words were then stored in their respective locations in the register Y (feasibility of such storage is ensured by the re-arrangement phase). This approach to FFT computation helps in reducing its memory footprint as we use only a single butterfly and only two register banks (each containing 256 data words each 32 bits long) for the entire operation.…”

Fast Algorithm for Computing the Discrete Hartley Transform of Type-II

“…Over last years, the discrete Hartley transform (DHT) has gained popularity in the fields of digital signal and image processing, as it possesses many desirable properties, used in many applications [1][2][3]. In general, there are four types of this transform known as type-I, -II, -III and -IV DHTs respectively.…”