Time-domain Aliasing Research Articles

Multisignal Modulation Classification Using Sliding Window Detection and Complex Convolutional Network in Frequency Domain

With the development of the Internet of Things (IoT), the IoT devices are increasing day by day, resulting in increasingly scarce spectrum resources. At the same time, many IoT devices are facing inevitable malicious attacks. The cognitive Radio-enabled IoT (CR-IoT) is proposed as an effective method for spectrum resource allocation and risk monitoring in the IoT. The signal detection and modulation recognition are the key technologies for CR-IoT, addressing the problem of multisignal detection and automatic modulation classification (AMC) is one of the prerequisites for realizing secure dynamic spectrum access. Based on sliding window and deep learning (DL), this study proposes a multisignal frequency domain detection and recognition method. The frequency spectrum of the time-domain overlapping signal is obtained through the fast Fourier transform (FFT), and the frequency spectrum is segmented based on the signal energy detection method. Finally a complex convolutional neural network (CNN) is constructed for the identification of signal spectrum information. The proposed method can recognize 264 time-domain aliasing and frequency-closed signals with an accuracy of 97.3% under the influence of −2 dB corresponding to the noise of the calibration signal. In addition, the proposed method eliminates the influence of bandwidth, which can effectively detect and recognize the signal types of each component in the frequency band. This method has wide applicability and provides an effective scheme for the IoT cognitive technology.

Low resolution fourier synthesis modelling for underwater acoustic channel impulse response

Fourier synthesis is the most widely used method for underwater acoustic broadband modeling. Traditionally, high frequency resolution and large time window length are needed to generate broadband time series to avoid aliasing in time domain. An optimized Fourier synthesis method is presented in this paper to accelerate the impulse response function modelling. The method consists of two steps, the phase-frequency response reconstruction and the impulse response function time window determination. The impulse response function of a range-dependent ocean channel is modeled using the proposed method with different frequency resolutions and compared with the interpolation method and traditional Fourier synthesis method. Modeling results show that the proposed method requires only a tenth of the frequency resolution of the traditional Fourier synthesis method and the correlation coefficients of modelling output time series are preserved above 95%. The proposed method also exhibits better phase response reconstruction performances than the interpolation method when the frequency resolution equals to 1 Hz.

High squint multichannel SAR imaging algorithm for high speed maneuvering platforms with small-aperture

For high speed maneuvering platforms, multichannel synthetic aperture radar (SAR) can realize wide-swath imaging more flexibly at a high squint. In this mode, the signal reconstruction and imaging is a challenging task because the direction of the channel array vector is time-variant and inconsistent with the radar velocity vector. In this paper, the properties of space time spectrum are analyzed in detail at first. It is found that the space time spectrum of the signal is irregular, in which the space time spectral lines are nonlinear and there is a massive Doppler spectrum shift. Therefore, a range-dependent signal reconstruction method based on space time spectrum correction is proposed to obtain the unambiguous Doppler spectrum. For wide-swath data processing, an improved Omega-K approach based on time domain spectrum compression is further proposed to obtain a well-focused image. A modified Stolt mapping is used to address the range variations of range cell migration (RCM). Subsequently, a time domain spectrum compression function is used to eliminate the time domain aliasing of small-aperture data without zero-padding. Simulation results and real data processing are presented to validate the proposed algorithm.

Study on Full Aperture Imaging Algorithm for Airborne TOPS Mode

The beam-scan allows the terrain observation by progressive scans (TOPS) mode to cover large azimuthal scenes in a short time, which also causes aliasing in both Doppler domain and azimuth time domain. In the TOPS mode, the most popular solution to overcome the aliasing problem is the “sub-aperture” method, which introduces sub-aperture partition and stitching operations. Aiming at an airborne digital array frequency modulated continuous wave (FMCW) SAR system, this paper discusses the removal of azimuth aliasing in the TOPS mode based on a full aperture imaging structure, by analyzing the Doppler characteristics of the echo signal of the airborne TOPS mode, the aliasing problem in the Doppler domain is avoided by properly setting system working parameters, which simplifies the imaging procedure; in addition, drawing up the idea of the de-rotation operation, we propose an improved frequency scaling algorithm, which removes the aliasing in the azimuth time domain without increasing the amount of processing data, and the algorithm contains only fast Fourier transformation and complex multiplication operations. The simulation results show that the algorithm can achieve the well-focused images of the airborne TOPS mode even in the case of serious aliasing in the azimuth time domain.

Time-domain aliasing and anti-aliasing effects in differentiating a band-unlimited signal

In this paper, we investigate time-domain errors occurring in the two extreme discrete-time differentiation modes of band-unlimited signals: in the full-band processing mode and in the processing mode with ideal anti-aliasing filtering (AAF) with a cut-off at the Nyquist frequency. We disclosed that regardless sampling frequency the error from AAF is greater than the aliasing error. It is found that type IV differentiators designed by three commonly known digital filter design methods approximately equally process the high frequency portion of the signal above the Nyquist frequency with nearly equal aliasing errors having a weak dependence on differentiator length. In contrast, the differentiators very differently compute the derivatives of the low frequency portion bellow the Nyquist frequency providing rather dissimilar the common differentiation accuracy. The results show that the differentiators derived by using maximal linearity constraints are more accurate than those designed by the Parks-McClellan algorithm and the impulse response truncation method.

Spatial Filtering Based on Differential Spectrum for Improving ML DOA Estimation Performance

Recently, maximum spatial eigenfiltering allowed significant improvements on the estimation performance of maximum likelihood direction-of-arrival (DOA) estimators for closely spaced sources. However, that eigenfilter may greatly attenuate widely spaced sources as SNR decreases, leading to severe performance degradation. Since the differential spectrum shows prominent spectral peaks around the true DOA angles even at very low SNR, we originally propose using it to derive two eigenvalue-based finite-impulse response spatial filters to overcome that problem. The first one employs the frequency sampling approach, whereas the second one includes moving average modeling, to fit the frequency response to the differential spectrum. Both the amount of spectral samples and the filter orders were carefully chosen to control aliasing in time domain and reduce the overall computational effort. The simulation results showed that the proposed filters preserved signal passbands of DOA sources, even where the maximum spatial eigenfilter failed. Compared with that filter, our propositions significantly reduced the threshold SNR for widely spaced sources while performing very similarly for closely spaced sources, at the expense of an small increase in runtime. To the best of our knowledge, the proposed filters are the first to allow spatial filtering in maximum likelihood DOA estimation independently of source separation.

Time-Domain Integral Equation Analysis of Electromagnetic Coupling through an Aperture Into a Parallel-Plate Waveguide Filled With a Lossy and Dispersive Dielectric

This paper proposes an efficient time-domain method to solve the method-of-moments-formulated integral equation pertinent to electromagnetic coupling through an aperture into a parallel plate waveguide (PPW) filled with a lossy and dispersive dielectric. The proposed method utilizes a fast Fourier transform-accelerated marching-on-in-time algorithm as a solution framework. Appropriate numerical procedures are introduced to avoid the adverse numerical effects associated with frequency-domain windowing and time-domain aliasing when convolving the time-domain Green's function of PPW with the derivative and integral of the respective temporal basis functions. The accuracy of the proposed method is confirmed by comparing the results of a circular, multiple square-shape apertures and a square aperture with those obtained using a commercial finite integration technique and a frequency-domain solver.

Audio Coding Using Overlap and Kernel Adaptation

Perceptual audio coding schemes typically apply the modified discrete cosine transform (MDCT) with different lengths and windows, and utilize signal-adaptive switching between these on a perframe basis for best subjective performance. In previous papers, the authors demonstrated that further quality gains can be achieved for some input signals using additional transform kernels such as the modified discrete sine transform (MDST) or greater inter-transform overlap by means of a modified extended lapped transform (MELT). This work discusses the algorithmic procedures and codec modifications necessary to combine all of the above features—transform length, window shape, transform kernel, and overlap ratio switching—into a flexible input-adaptive coding system. It is shown that, due to full time-domain aliasing cancelation, this system supports perfect signal reconstruction in the absence of quantization and, thanks to fast realizations of all transforms, increases the codec complexity only negligibly. The results of a 5.1 multichannel listening test are also reported.

Harmonic Enhancement in Low Bitrate Audio Coding Using an Efficient Long-Term Predictor

This paper proposes audio coding using an efficient long-term prediction method to enhance the perceptual quality of audio codecs to speech input signals at low bit-rates. The MPEG-4 AAC-LTP exploited a similar concept, but its improvement was not significant because of small prediction gain due to long prediction lags and aliased components caused by the transformation with a time-domain aliasing cancelation (TDAC) technique. The proposed algorithm increases the prediction gain by employing a deharmonizing predictor and a long-term compensation filter. The look-back memory elements are first constructed by applying the de-harmonizing predictor to the input signal, then the prediction residual is encoded and decoded by transform audio coding. Finally, the long-term compensation filter is applied to the updated look-back memory of the decoded prediction residual to obtain synthesized signals. Experimental results show that the proposed algorithm has much lower spectral distortion and higher perceptual quality than conventional approaches especially for harmonic signals, such as voiced speech.

Discrete-signal analysis and design

Introduction. 1. Define the goals of the book. 2. Define discrete signals. 3. The advantages of discrete-signal analysis and design. 4. Describe the DFT and IDFT. 5. Discuss the Mathcad program. 6. Discuss MATLAB and less expensive approaches. 7. Discuss Multisim program from National Instruments Co. 8. Discuss the Mathtype program. 9. Mention LabVIEW. 10. Mention Search Engines. 11. Discuss the personal productivity software capability. Chapter 1: First Principles 1. Sequence structure in time domain and frequency domain. 2. Two-sided time and frequency. 3. The discrete Fourier transform. 4. The inverse discrete Fourier transform. 5. Frequency and time scaling. 6. Number of samples needed. 7. Complex frequency domain sequences. The phasor concept. 8. Time x(n) vs frequency X(k). Chapter 2: Sine, Cosine and Theta. 1. One-sided sequences. 2. Combinations of two-sided phasors 3. Time and spectrum transformations. 4. Transforming two-sided phasor sequences into one-sided sine, cosine, THETA. 5. Example 2-1, nonlinear amplifier distortion and square law modulator. 6. Example 2-2, analysis of the ramp function. Chapter 3: Spectral Leakage and Aliasing. 1. Spectral leakage. Non-integer values of time and frequency. 2. Scaling of frequency reduces leakage. Example 3-1. 3. Aliasing in the two-sided frequency domain. 4. Aliasing in the positive frequency domain. 5. Example 3-2. Analysis of frequency domain aliasing. 6. Time domain aliasing. Chapter 4: Smoothing and Windowing. 1. Smoothing the rectangular window, without noise and with noise. 2. Smoothed sequences near the beginning and end. 3. Signal to noise ratio of a smoothed sequence. 4. Three-point smoothing and seven point smoothing. 5. Windowing in the time and frequency domains. 6. The rectangular window (review Ch. 3). 7. The Hamming Window. 8. The Hanning (Hann) Window. 9. Relative merits of the three windows. 10. Lobe amplitudes of the three types of windows. 11. Behavior of windows near k = 1 and 2. 12. Scaling the windows for improved frequency resolution. Chapter 5: Multiplication and Convolution 1. Sequence multiplication. 2. Polynomial multiplication. 3. Discrete Convolution basic equation. 4. Relating convolution to polynomial multiplication. 5. The fold and slide concept. 6. Circular discrete convolution (try to avoid). 7. Sequence time and phase shift. 8. The DFT and IDFT of discrete convolution. 9. Fig 5-6. Compare convolution and multiplication. 10. De-convolution. Chapter 6: Probability and Correlation 1. Expected value of noiseless sequence. 2. Include some additive noise. 3. Envelope detection of noisy sequence. 4. Power of noiseless sequence. 5. Power of noisy sequence. 6. Sequence averaging. 7. Variance (AC component). 8. Gaussian (normal) distribution. 9. Cumulative distribution (CDF). 10. Autocorrelation of a sequence. 11. Cross correlation of two sequences. 12. Auto-covariance. 13. Cross-covariance. 14. Correlation coefficient. Chapter 7: Power spectrum. 1. Finding the power spectrum using Eq 7-1. 2. Two-side phasor spectrum, one-side power spectrum. 3. Example 7-1. See Fig 7-2. 4. Random Gaussian noise spectrum. 5. Measuring power spectrum. 6. Spectrum analyzer example. 7. Wiener-Kintchine theorem. 8. System power transfer Eq 7-6. 9. Cross power spectrum. 10. Example of calculating phase noise. Chapter 8: Hilbert Transform. 1. The perfect Hilbert transformer. 2. Example of a Hilbert transform of a square wave. 3. Illustrate smoothing of the Example. 4. Explanation of peaks in Hilbert of square wave. 5. Mathematics of the Hilbert transform. 6. The analytic signal. 7. Example of construction of analytic signal. 8. Single-sideband RF signals. 9. SSB design. 10. The basic all-pass network. 11. -90- cascaded phase shift audio network. 12. Why the -90- network is not equivalent to a Hilbert transformer. 13. Filter method SSB transmitter. 14. Phasing method SSB receiver. 15. Filter method SSB receiver. Appendix A: Additional discrete-signal information 16. Discrete derivative. 17. State variable solutions. 18. Using the discrete derivative. Glossary. Index.

System and method for efficient time-domain aliasing cancellation

The invention comprises an efficient system and method for performing the modified discrete cosine transform (MDCT) in support of time-domain aliasing cancellation (TDAC) perceptive encoding compression of digital audio. In one embodiment, an AC-3 encoder performs a required time-domain to frequency-domain transformation via a MDCT. The AC-3 specification presents a non-optimized equation for calculating the MDCT. In one embodiment of the present invention, an MDCT transformer (230) is utilized which produces the same results as carrying out the calculations directly as in the AC-3 equation, but requires substantially lower computational resources. Because the TDAC scheme requires MDCT calculations on differing block sizes, called the long and short blocks, one embodiment of the present invention utilizes complex-valued premultiplication and postmultiplication steps which prepare and arrange the data samples so that both the long and short block transforms may be computed with a computationally efficient FFT. The premultiplication and postmultiplication steps are carefully structured to work with FFT's in a manner which will give the same numeric results as would be achieved with a direct calculation of the MDCT.

Time-domain aliasing cancellation role in error concealment

A new method to enhance the error concealment of single AAC frame loss is presented. This scheme exploits the time-domain aliasing cancellation property of the MDCT-based audio coder. A mean square error improvement of approximately 10 dB is achieved. The advantage of this method over the frame repetition technique that has the same computational weight is highlighted.

Linear-quadratic system identification with completed frequency domain region of support

In general, aliasing exists in the output of discrete-time nonlinear systems due to the higher order harmonics and intermodulation among inputs. If the input is allowed to cover the full range from DC to half the sample rate, the aliased components in the output must be taken into account for accurate system identification. We have extended a known system identification method to account for these aliased terms by completing the region of support for the quadratic transfer function. We also present a method for preventing a form of time domain aliasing. Together, these approaches can lead to significantly improved system characterization with less data as compared to current techniques.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis/Synthesis filter bank design based on time domain aliasing cancellation

A single-sideband analysis/synthesis system is proposed which provides perfect reconstruction of a signal from a set of critically sampled analysis signals. The technique is developed in terms of a weighted overlap-add method of analysis/synthesis and allows overlap between adjacent time windows. This implies that time domain aliasing is introduced in the analysis; however, this aliasing is cancelled in the synthesis process, and the system can provide perfect reconstruction. Achieving perfect reconstruction places constraints on the time domain window shape which are equivalent to those placed on the frequency domain shape of analysis/synthesis channels used in recently proposed critically sampled systems based on frequency domain aliasing cancellation [7], [8]. In fact, a duality exists between the new technique and the frequency domain techniques of [7] and [8], The proposed technique is more efficient than frequency domain designs for a given number of analysis/synthesis channels, and can provide reasonably band-limited channel responses. The technique could be particularly useful in applications where critically sampled analysis/synthesis is desirable, e.g., coding.