Real-time Sample Rate Converter Using Gaussian Convolution Kernel
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Solution Overview
Problem
Real-time sample rate converters in digital audio and audio-video systems face challenges in minimizing harmonic distortion, achieving linear phase response, and reducing circuit power and computation costs, especially when dealing with irrational and time-varying sample rate ratios.
Innovation Solution
A real-time sample rate converter using a non-polynomial gaussian function as a convolution kernel for sample rate conversion, which can be truncated after a small number of terms, reducing the number of input samples required and employing a CORDIC algorithm for efficient computation, thereby minimizing distortion and power consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If higher-order polynomial functions are used to reduce error in sample rate conversion, then manufacturing precision is improved, but device complexity and computation time increase
Solution Approach 1:
The patent changes the mathematical function type from polynomial to Gaussian non-polynomial function. This parameter change in the kernel function allows achieving high conversion precision while requiring fewer filter taps, thus reducing device complexity and computation time compared to traditional higher-order polynomial approaches
Solution Approach 2:
The patent extracts and utilizes the rapid decay property of the Gaussian function to truncate the convolution sum after a small number of terms. This extraction of the decay characteristic allows achieving acceptable precision with minimal computational effort, avoiding the complexity of full high-order polynomial processing
2Manufacturing precision
If a large number of filter taps are used to reduce distortion, then manufacturing precision is improved, but use of energy increases
Solution Approach 1:
By changing from polynomial to Gaussian function, the patent achieves the same or better conversion accuracy with significantly fewer filter taps. The Gaussian function's rapid decay allows truncating the convolution sum early, dramatically reducing the number of multiplications and additions required, thus lowering computation power and energy consumption
Solution Approach 2:
The patent applies partial action by truncating the infinite convolution sum after a small number of terms. Due to the Gaussian function's rapid decay, this partial summation achieves acceptable precision without requiring the full computational effort of processing all terms, thereby reducing energy consumption while maintaining sufficient accuracy
3Use of energy by moving object
If IIR filters are used to reduce the number of taps, then use of energy is reduced, but manufacturing precision deteriorates due to non-linear group delay
Solution Approach 1:
The patent changes the filter type from IIR to FIR with Gaussian kernel. This parameter change maintains linear phase response (preserving manufacturing precision) while still achieving low power consumption through the rapid decay property of the Gaussian function that allows using fewer taps compared to traditional FIR filters
Solution Approach 2:
The patent combines the advantages of FIR filters (linear phase response) with the efficiency of IIR filters (low computation) by using a Gaussian kernel in the FIR convolution. This composite approach creates a filter that has both the phase linearity of FIR and the computational efficiency needed for low power consumption
4Adaptability or versatility
If intermediate sample rate conversion is used to achieve flexible sampling rate ratios, then adaptability is improved, but use of energy increases due to high-speed circuits
Solution Approach 1:
The patent changes the conversion approach by using a Gaussian kernel with variable standard deviation parameter instead of fixed intermediate sample rate conversion. This parameter change allows the filter to adapt to different sampling rate ratios directly without requiring high-speed intermediate rate circuits, thereby maintaining flexibility while reducing power consumption
Data Source
AI summary
A real-time sample rate converter having a non-polynomial convolution kernel provides reduction in die area and power for performing sample rate conversion in real-time. A non-polynomial convolution kernel, which may be a gaussian operator, is used to determine output sample values from values of an incoming stream of values. If the input sample rate is higher than the output sample rate, the input sample stream is convolved with the gaussian kernel and then decimated to yield the output stream. If the input sample rate is lower than the output sample rate, the input stream is resampled to a small multiple of the output sample rate and convolved with the gaussian kernel to produce the output sample stream directly.