Spectral subtraction was one of the first algorithms proposed for speech enhancement, with more papers being written about it than any other algorithm. The basic principle is as follows: if we assume additive noise, then we can subtract the noise spectrum from the noisy speech spectrum, so we are left with what should look like the clean speech spectrum. For this we need to know what the noise spectrum looks like, so we estimate it during regions of no speech (parts of the signal that contain only noise) and then assume it won't change much from frame to frame.
The first step in spectral subtraction is to frame the speech signal into short, overlapping frames. Typically frames are taken to be about 20ms long. For a 16kHz sampled audio file, this corresponds to 0.020s * 16,000 samples/s = 400 samples in length. We then use an overlap of 50%, or about 200 samples. This means the first frame starts at sample 0, the second starts at sample 200, the third at 400 etc.
Now that we have the magnitude for each frame and a noise estimate, we can proceed with the meat of spectral subtraction: subtracting the noise estimate. This is done in the following way (here we use to represent the estimated clean spectrum, for the noisy spectrum we actually see, and for our noise estimate):
Now we need to do the IFFT (inverse FFT) of and do overlap add of the resulting time-domain frames to reconstruct our original signal. That is pretty much all there is to spectral subtraction, though there are many slight modifications that change the quality of the resulting enhanced speech.
In the discussion above, we have defined magnitude spectral subtraction. Another closely related concept is power spectral subtraction, which we can see if we write the subtraction equation like this:
For we have magnitude spectral subtraction, but for we have power spectral subtraction. Alternatively you could have or . Each of these will have slightly different characteristics as far as noise suppression vs. loss of speech information goes.
The common audio noise reduction approaches built-in to things like Audacity are based around spectral subtraction, which estimates the level of steady background noise in the Fourier transform magnitude domain, then removes that much energy from every frame, leaving energy only where the signal \"pokes above\" this noise floor.
Multiband spectral subtraction as proposed by Kamath 2002. Uses adjusts the subtraction coefficient with the frequency as well as the SNR. note that the first 0.25sec of your signal is used to model the noise.
I'm assuming since you didn't say that you're working with audio. But my answer generally applies if you're working with images/video as well. Unless the background you're trying to subtract is exactly the same, I doubt subtracting a phase-inverted version of the signal will work. It sounds like what you're trying to perform is spectral subtraction. This is a common technique where you simply subtract the average FFT magnitude spectrum from your signal. See this paper on spectral subtraction. If working with images/video, I assume that you could do this in 2 dimensions as well and the math would be similar.
Abstract:In this paper, a new pipelined architecture of the multi-band spectral subtraction algorithm has been proposed for real-time speech enhancement. The proposed hardware has been implemented on field programmable gate array (FPGA) device using Xilinx system generator (XSG), high-level programming tool, and Nexys-4 development board. The multi-band algorithm has been developed to reduce the additive colored noise that does not uniformly affect the entire frequency band of useful signal. All the algorithm steps have been successfully implemented on hardware. Pipelining has been employed on this hardware architecture to increase the data throughput. Speech enhancement performances obtained by the hardware architecture are compared to those obtained by MATLAB simulation using simulated and actual noises. The resource utilization, the maximum operating frequency, and power consumption are reported for a low-cost Artix-7 FPGA device.Keywords: FPGA; hardware/software co-simulation; pipelining; speech enhancement; multi-band spectral subtraction; signal-to-noise ratio
Along with the characteristics of the light source and the surface material, the radiation values measured by the sensor are influenced by the sensor gain and bias (offset) at each spectral wavelength. The raw data recorded by the hyperspectral sensors is known as the digital numbers (DNs). To use the hyperspectral data for quantitative analysis, you must calibrate the data for TOA radiance values, and estimate the actual surface reflectance values from the DNs.
You can find the TOA radiance values for uncalibrated hyperspectral data by using the dn2radiance function. The function reads the gain and the bias (offset) values for each spectral band from the header file associated with the hyperspectral data.
Dark pixel subtraction or dark object subtraction, is an empirical method suitable for removing atmospheric haze from hyperspectral images. Atmospheric haze is characterized by high DN values, and results in unnatural brightening of the images. The dark pixels are minimum values pixels in each band. Dark pixels are assumed to have zero surface reflectance, and their values account for the additive effect of the atmospheric path radiance.
Internal average relative reflectance (IARR) is an empirical approach that computes relative surface reflectance by normalizing each pixel spectrum with the mean spectrum. The method assumes that the surface is heterogeneous, and the spectral reflectance characteristics cancel out. As a result, the mean spectrum of the surface is similar to a flat field spectrum.
Use the fast in-scene method to correct atmospheric effects on hyperspectral data with diverse pixel spectra and sufficient number of dark pixels. The method estimates the baseline spectrum by using the dark pixels.
A VOICE ACTIVITY DETECTOR USING THE CHI-SQUARE TEST\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n EBB Chapter 2 SIGNALS AND SPECTRA Chapter Objectives: Basic signal properties (DC, RMS, dBm, and power); Fourier transform and spectra; Linear systems.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Nico De Clercq Pieter Gijsenbergh Noise reduction in hearing aids: Generalised Sidelobe Canceller.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n DIGITAL IMAGE PROCESSING Instructors: Dr J. Shanbehzadeh M.Gholizadeh M.Gholizadeh\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Page 0 of 23 MELP Vocoders Nima Moghadam SN#: Saeed Nari SN#: Supervisor Dr. Saameti April 2005 Sharif University of Technology.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Reduction of Additive Noise in the Digital Processing of Speech Avner Halevy AMSC 663 Mid Year Progress Report December 2008 Professor Radu Balan 1.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Pitch-synchronous overlap add (TD-PSOLA)\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Nico De Clercq Pieter Gijsenbergh. \\uf0a1 Problem \\uf0a1 Solutions \\uf0a7 Single-channel approach \\uf0a7 Multichannel approach \\uf0a1 Our assignment Overview.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n The Physical Layer Lowest layer in Network Hierarchy. Physical transmission of data. \\u2013Various flavors Copper wire, fiber optic, etc... \\u2013Physical limits.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n INF380 - Proteomics-101 INF380 \\u2013 Proteomics Chapter 10 \\u2013 Spectral Comparison Spectral comparison means that an experimental spectrum is compared to theoretical.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Authors: Sriram Ganapathy, Samuel Thomas, and Hynek Hermansky Temporal envelope compensation for robust phoneme recognition using modulation spectrum.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n 1 Robust Endpoint Detection and Energy Normalization for Real-Time Speech and Speaker Recognition Qi Li, Senior Member, IEEE, Jinsong Zheng, Augustine.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Chapter 6. Effect of Noise on Analog Communication Systems\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n ECE 5525 Osama Saraireh Fall 2005 Dr. Veton Kepuska\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n 23 November Md. Tanvir Al Amin (Presenter) Anupam Bhattacharjee Department of Computer Science and Engineering,\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Noise Reduction Two Stage Mel-Warped Weiner Filter Approach.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Ch5 Image Restoration CS446 Instructor: Nada ALZaben.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Study of Broadband Postbeamformer Interference Canceler Antenna Array Processor using Orthogonal Interference Beamformer Lal C. Godara and Presila Israt.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n P. N. Kulkarni, P. C. Pandey, and D. S. Jangamashetti \\/ DSP 2009, Santorini, 5-7 July DSP 2009 (Santorini, Greece. 5-7 July 2009), Session: S4P,\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n 0 - 1 \\u00a9 2007 Texas Instruments Inc, Content developed in partnership with Tel-Aviv University From MATLAB \\u00ae and Simulink \\u00ae to Real Time with TI DSPs Spectrum.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n IIT Bombay ICSCI 2004, Hyderabad, India, Feb\\u2019 04 Introduction Analysis \\/ synthesis Spec. Sub. Methodology Results Conclusion and.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Voice Activity Detection based on OptimallyWeighted Combination of Multiple Features Yusuke Kida and Tatsuya Kawahara School of Informatics, Kyoto University,\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n ICASSP 2006 Robustness Techniques Survey ShihHsiang 2006.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n EEL 6586: AUTOMATIC SPEECH PROCESSING Speech Features Lecture Mark D. Skowronski Computational Neuro-Engineering Lab University of Florida February 27,\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n Digital Audio Signal Processing Lecture-3 Noise Reduction\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n 1 Introduction1 Introduction 2 Noise red. tech 3 Spect. Subtr. 4. QBNE 5 Invest. QBNE 6 Conc., & future work2 Noise red. tech 3 Spect. Subtr.4. QBNE5 Invest.\\n \\n \\n \\n \\n \",\" \\n \\n \\n \\n \\n \\n APPLICATION OF A