The calculation of cross-correlation between a sequence with good autocorrelation and its decimated sequence is an interesting problem in the field of sequence design. In this letter, we consider a class of ternary sequences with perfect autocorrelation, proposed by Shedd and Sarwate (IEEE Trans. Inf. Theory, 1979, DOI: 10.1109/TIT.1979.1055998), which is generated based on the cross-correlation between m-sequence and its d-decimation sequence. We calculate the cross-correlation distribution between a certain pair of such ternary perfect sequences and show that the cross-correlation takes three different values.

Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.

In Xu, Chen, and Liu's letter, two constructions producing perfect 8-QAM+/8-QAM sequences were given. We show that their constructions are equivalent to Zeng, et al.'s constructions under unit constant transform. Since the autocorrelation of a perfect sequence under unit constant transform is invariable, Xu, et al.'s constructions are the special case of Zeng, et al.'s constructions.

Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg {rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.

In this paper, we show that if the d-decimation of a (q-1)-ary Sidelnikov sequence of period q-1=pm-1 is the d-multiple of the same Sidelnikov sequence, then d must be a power of a prime p. Also, we calculate the crosscorrelation magnitude between some constant multiples of d- and d'-decimations of a Sidelnikov sequence of period q-1 to be upper bounded by (d+d'-1)√q+3.

This paper proposes a method for evaluating visual differences caused by decimation. In many applications it is important to evaluate visual differences of two different images. There exist many image assessment methods that utilize the model of the human visual system (HVS), such as the visual difference predictor (VDP) and the Sarnoff visual discrimination model. In this paper, we extend and elaborate on the conventional image assessment method for the purpose of evaluating the visual difference caused by the image decimation. Our method matches actual human evaluation more and requires less computational complexity than the conventional method.

This paper presents a fully differential third-order (2-1) switched-current (SI) cascaded delta-sigma modulator (DSM), with an analog error cancellation logic circuit, and a digital decimation filter that is fabricated using 0.18-µm CMOS technology. The 2-1 architecture with only the quantizer input being fed into the second stage is introduced not only to reduce the circuit complexity, but also to be implemented easily using the switched-current approach. Measurements reveal that the dominant error is the quantization error of the second one-bit quantizer (e2). This error can be eliminated using an analog error cancellation logic circuit. In the proposed differential sample-and-hold circuit, low input impedance is presented with feedback and width-length adjustment in SI feedback memory cell (FMC); and that a coupled differential replicate (CDR) common-mode feedforward circuit (CMFF) is used to compensate the error of the current mirror. Also, measurements indicate that the signal-to-noise ratio (SNR), dynamic range (DR), effective number of bits (ENOB), power consumption and chip size are 67.3 dB, 69 dB, 10.9 bits, 12.3 mW, and 0.200.21 mm2, respectively, with a bandwidth of 40 kHz, a sampling rate of 10.24 MHz, an OSR of 128 and a supply voltage of 1.8 V.

Partial transmit sequence (PTS) is a well known technique used to reduce the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) signal. However, it has relatively high complexity due to the computation of multiple inverse fast Fourier transforms (IFFTs). To reduce this complexity, we use intermediate signals within a decimation in frequency (DIF) radix IFFT and propose a new PTS subblocking technique which requires the computation of only partial IFFTs. Performance results are presented which show a PAPR reduction similar to that with other techniques such as original PTS (O-PTS). Further, we show that complexity reduction can be achieved with either low or high radix IFFT algorithms.

In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) radios, sequences with low correlation and large family size are important for reducing multiple access interference (MAI) and accepting more active users, respectively. In this paper, a new collection of families of sequences of length pn-1, which includes three constructions, is proposed. The maximum number of cyclically distinct families without GMW sequences in each construction is , where p is a prime number, n is an even number, and n=2m, and these sequences can be binary or polyphase depending upon choice of the parameter p. In Construction I, there are pn distinct sequences within each family and the new sequences have at most d+2 nontrivial periodic correlation {-pm-1,-1,pm-1,2pm-1,,dpm-1}. In Construction II, the new sequences have large family size p2n and possibly take the nontrivial correlation values in {-pm-1,-1,pm-1,2pm-1,,(3d-4)pm-1}. In Construction III, the new sequences possess the largest family size p(d-1)n and have at most 2d correlation levels {-pm-1,-1,pm-1,2pm-1,,(2d-2)pm-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, WR d, WR 3d-4 and WR 2d-2, respectively. Each family in Constructions I, II and III contains a GMW sequence. In addition, Helleseth sequences and Niho sequences are special cases in Constructions I and III, and their restriction conditions to the integers m and n, pm≠ 2(mod 3) and n≡ 0 (mod 4), respectively, are removed in our sequences. Our sequences in Construction III include the sequences with Niho type decimation 32m-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

In DS-CDMA systems and DS-UWB radios, low correlation of spreading sequences can greatly help to minimize multiple access interference (MAI) and large linear span of spreading sequences can reduce their predictability. In this letter, new sequence sets with low correlation and large linear span are proposed. Based on the construction Tr1m[Trmn(αbt+γiαdt)]r for generating p-ary sequences of period pn-1, where n=2m, d=upm v, b=u v, γi GF(pn), and p is an arbitrary prime number, several methods to choose the parameter d are provided. The obtained sequences with family size pn are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (u+v-1)pm-1. The simulation by a computer shows that the linear span of the new sequences is larger than that of the sequences with Niho-type and Welch-type decimations, and similar to that of [10].

As a fundamental building block of multirate systems, the downsampler, also known as the decimator, is a periodically time-varying linear system. An eigensignal of the downsampler is defined to be an input signal which appears at the output unaltered or scaled by a non-zero coefficient. In this paper, the eigensignals are studied and characterized in the time and z domains. The time-domain characterization is carried out using number theoretic principles, while the one-sided z-transform and Lambert-form series are used for the transform-domain characterization. Examples of non-trivial eigensignals are provided. These include the special classes of multiplicative and completely multiplicative eigensignals. Moreover, the locus of poles of eigensignals with rational z transforms are identified.

In this letter, we investigate a decimated selective mapping (SLM) method for the peak-to-mean envelope power ratio (PMEPR) reduction in an OFDM system. Under the condition of the same side information (SI) bits, the SLM can be implemented by decimating OFDM samples, which is less complex compared to the ordinary SLM incurring a slight degradation of the PMEPR performance. The decimated SLM (DSLM) approach can be generalized to a multiple-antenna OFDM system employing a space-time block coding (STBC).

The software-defined radio technique translates the traditional hardware radio platform to a flexible software radio platform that can support multiple air interface standards. This work proposes an efficient IF processing architecture based on software-defined radio for 2G GSM/IS-95 and 3G W-CDMA systems. Hardware complexity is estimated by fixed-point simulation. IF processing architecture should be highly flexible and minimally complex. Firstly, a carrier channel is selected from a wide frequency band using a high-resolution numerically controlled oscillator (NCO). Wide-range interpolation/decimation is performed by the cascaded integrator comb (CIC) filter that involves no multiplier nor stores filter coefficients. Both the desired narrowband and the desired wideband signals can be extracted. The look-up table (LUT), based on the distributed arithmetic (DA) algorithm is used to implement the finite impulse response (FIR) filter. Therefore, a small area and high speed can be achieved. The errors caused by truncation, quantization, rounding-off and overflow are predicted using a fixed-point simulation. These predictions will help to evaluate the word-length for VLSI implementation. Finally, ALTERA APEX20KE is used as a target device. One hundred thousand gates are used for the implementation. Thus, the proposed architecture has high processing flexibility and small area.

We investigated single flux quantum sinc filters with multistage decimation structure in order to realize high-speed sinc filter operation. Second- and third-order (k=2, 3) sinc filters with a decimation factor N=2 were designed and confirmed their proper operations. These sinc filters with N=2 are utilized as elementary circuit blocks of our multistage decimation sinc filters with N=2M, where M indicates the number of the stage of the decimation. As an example of the multistage decimation filter, we designed a k=2, N=4 sinc filter which was formed from a two-stage decimation structure using k=2, N=2 sinc filters, and confirmed its proper operation. The k=2, N=4 sinc filter consisted of 1372 Josephson junctions with the power consumption of 191 µW.

In this paper, we describe our SFQ circuit design and measurement carried out in SRL-ISTEC. We are studying an oversampling sigma-delta modulator and a counter-type decimation filter with multistage structure for developing AD converters for software-defined radio application. We are also developing a superconducting memory, whose peripheral circuits are constructed with SFQ circuits.

Phase-based methods for estimating the frequency of a sinusoid have typically suffered from a threshold effect, where for signal to noise ratio (SNR) below the threshold, the mean squared error of the estimate rapidly increases. Furthermore, it is a significant problem that the threshold is considerably high and strongly depends on frequency. To overcome the difficulties, a Kalman-based sinusoidal estimator bank (KSEB) is proposed. In the derivation of the KSEB, a four-channel filter bank and decimation technique are effectively used. The computer simulation also demonstrates the superiority of the KSEB to the other frequency estimators.

NOR self-decimated sequences are attractive for stream ciphers because they have a good statistical property and the hardware construction is very simple. This paper presents an analysis of NOR self-decimation system for any parameter. We first determine the period. Then we show the exact distribution of consecutive two bits and three bits, which are shown to be almost uniform distribution.

This paper presents a novel approach to pixel decimation for motion estimation in video coding. Early techniques of pixel decimation use regular pixel patterns to evaluate matching criterion. Recent techniques use adaptive pixel patterns and have achieved better efficiency. However, these adaptive techniques require an initial division of a block into a set of uniform regions and therefore are only locally-adaptive in essence. In this paper, we present a globally-adaptive scheme for pixel decimation, in which no regions are fixed at the beginning and pixels are selected only if they have features important to the determination of a match. The experiment results show that when no more than 40 pixels are selected out of a 1616 block, this approach achieves a better search accuracy by 13-22% than the previous locally-adaptive methods which also use features.