Convolution Reverb Bandwidth Reduction via Polar Coordinate Conversion
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Solution Overview
Problem
The computational cost and storage requirements for convolution of impulse response signals are high due to the use of high bit count complex numbers, which are inefficient for real-time applications and limited storage devices.
Innovation Solution
Converting impulse response signals from complex number form to polar coordinates and applying additional compression techniques, such as truncating high and low frequency bins and scaling amplitudes to 8-bit integers, reduces the file size by at least 50% without significant audio quality loss.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high bit count complex numbers are used to represent frequency spectra, then audio quality is maintained, but storage requirements and computational cost increase significantly
Solution Approach 1:
The patent changes the representation parameters of frequency spectra from high-bit complex numbers to low-bit polar coordinates. Each complex number is transformed into magnitude and phase components, which are then quantized to significantly fewer bits (e.g., 8-bit or 16-bit total per frequency bin instead of 32-bit or 64-bit complex numbers), achieving compression while maintaining perceptual audio quality.
Solution Approach 2:
Instead of storing complex numbers in the traditional rectangular form (real and imaginary parts), the patent inverts the approach by storing them in polar form (magnitude and phase). This inversion allows for more efficient compression because the magnitude and phase can be independently quantized and stored with fewer bits while preserving the essential audio information.
2Measurement precision
If high bit count complex numbers are used to represent frequency spectra, then audio quality is maintained, but computational cost increases
Solution Approach 1:
The patent changes the computational parameters by representing frequency spectra in polar coordinates rather than complex rectangular form. This parameter change reduces the computational complexity of convolution operations because multiplying polar representations involves simpler operations (adding phases and multiplying magnitudes) compared to complex number multiplication, thereby reducing computational cost while maintaining audio quality.
3Productivity
If frequency domain convolution techniques are used, then computational time is reduced compared to direct time domain convolution, but storage requirements for high precision spectra remain high
Solution Approach 1:
The patent applies parameter changes by representing frequency domain spectra in polar coordinates with reduced bit precision. This allows frequency domain convolution techniques to proceed with computationally efficient operations while simultaneously reducing storage requirements through low-bit representation of magnitude and phase values, thus resolving the contradiction between computational efficiency and storage requirements.
Data Source
AI summary
Frequency spectrum data of a segment of an input audio signal is converted from complex number form having a high bit count real and imaginary parts to polar coordinate form having a lower bit count angles and amplitudes. The frequency spectrum of the segment of the input audio signal is stored in the polar coordinate form. Storing the frequency spectrum of the segment of the input signal in polar coordinate form requires fewer bits than storing the frequency spectrum data of the segment of the input signal in complex number form.