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Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.
on-square matrix. It has a wide range
of applications especially in Multiple Input-Multiple Output (MIMO) communication
systems. Unfortunately it has high computation complexity { for matrix size of nxn,
QRD has O(n3) complexity and back substitution, which is used to solve a system
of linear equations, has O(n2) complexity. Thus, as the matrix size increases, the
hardware resource requirement for QRD and back substitution increases signicantly.
This thesis presents the design and implementation of a
exible QRD and back substitution accelerator using a folded architecture. It can support matrix sizes of
4x4, 8x8, 12x12, 16x16, and 20x20 with low hardware resource requirement.
The proposed architecture is based on the systolic array implementation of the
Givens algorithm for QRD. It is built with three dierent types of computation blocks
which are connected in a 2-D array structure. These blocks are controlled by a
scheduler which facilitates reusability of the blocks to perform computation for any
input matrix size which is a multiple of 4. These blocks are designed using two
basic programming elements which support both the forward and backward paths to
compute matrix R in QRD and column-matrix X in back substitution computation.
The proposed architecture has been mapped to Xilinx Zynq Ultrascale+ FPGA
(Field Programmable Gate Array), ZCU102. All inputs are complex with precision
of 40 bits (38 fractional bits and 1 signed bit). The architecture can be clocked at
50 MHz. The synthesis results of the folded architecture for dierent matrix sizes
are presented. The results show that the folded architecture can support QRD and
back substitution for inputs of large sizes which otherwise cannot t on an FPGA
when implemented using a
at architecture. The memory sizes required for dierent
matrix sizes are also presented.
The computationally intensive parts of temporal mitigation are identified and hardware accelerated. The hardware implementation is based on sequential approach with optimizations applied on the individual components for better performance.
An extensive analysis using a range of fixed point data types is performed to find the optimal data type necessary.
Finally a hybrid combination of data types for different components of temporal mitigation is proposed based on results from the above analysis.