Deve
  • Member for 9 years, 7 months
  • Last seen more than a week ago
Difference between discrete time fourier transform and discrete fourier transform
Accepted answer
20 votes

The discrete-time Fourier transform (DTFT) is the (conventional) Fourier transform of a discrete-time signal. Its output is continous in frequency and periodic. Example: to find the spectrum of the ...

View answer
Symmetry of real and imaginary parts in FFT
15 votes

Yes, this is always true if the input to the DFT is real valued. It's called the "conjugate complex symmetry", because $$ X_{N-n} = {X_n}^* $$ where $X_n$ is the DFT output and $()^*$ denotes the ...

View answer
FFT of sine wave not coming as expected i.e single point
15 votes

Acually Matt's answer already gives one view on the problem here: the DFT is implicitly periodic in both time and frequency domain (see this question). From your parameters we can calculate that your ...

View answer
What is the difference between Lumped and Distributed systems?
Accepted answer
11 votes

The elements building a lumped system are thought of being concentrated at singular points in space. The classical example is an electrical circuit with passive elements like resistor, inductance and ...

View answer
How is symbol synchronization with OFDM done?
9 votes

Regarding you're general question about how symbol sychronization is done in OFDM systems: One of the most popular and frequently used techniques is the transmission of one or several pilot symbols ...

View answer
how do I calculate SNR of noisy signal?
9 votes

The common definition of SNR is the power of the wanted signal divided by the noise power. Suppose you have obtained the wanted and the noise signal as arrays, calculation of the SNR in Matlab before ...

View answer
Why is `fftfilt` (i.e. `fft` of both inputs, then element-wise multiplication, then `ifft`) faster than direct convolution?
Accepted answer
8 votes

Whether the direct convolution or the FFT/IFFT method is faster depends on the length of the impulse response, $N_\mathrm{i}$ and the signal length $N_\mathrm{s}$. With the formulas taken from here I'...

View answer
Fourier Transform Identities
8 votes

Yes, if eqs. (2) and (3) hold for any "type of signal" (which they do), then (5) must hold. Inserting (4) into (2) we get $$ \mathscr{F}\big\{x^*(t)\big\} = X(-f) $$ and using (3) $$ X(-f) = X^*(-f) ...

View answer
Is $x(t) = \cos t + \sin\left(\frac{1}{2}t\right)$ a periodic signal?
8 votes

As for every $t_0\in\mathbb{R}$ and $k\in\mathbb{Z}$ $$ \begin{eqnarray} &x(t_0+4k\pi) &=\cos(t_0+4k\pi)+\sin(t_0/2+2k\pi)\\ & &=\cos(t_0)+\sin(t_0/2)\\ & ...

View answer
Why not use zero-signal in digital transmission?
8 votes

All implementation aspects aside, the constellation you propose performs worse than QPSK in an additve white gaussian noise (AWGN) channel. I claim this based on simulations that I have run with ...

View answer
How does averaging increase the Signal to Noise ratio?
Accepted answer
8 votes

Intuitively this is true, because averaging a zero mean noise processes approximates its expectation value - which is zero. More rigorously: If the signal $x$ that you want to observe (estimate, ...

View answer
Nyquist Frequency Phase Shift
7 votes

The sampling theorem states that $f_\mathrm{S} \geq 2f_\mathrm{max}$, where $f_\mathrm{S}$ and $f_\mathrm{max}$ are the sampling and maximum signal freuqency, respectively. But there's an additional ...

View answer
Finding out modulation index and DC offset
Accepted answer
6 votes

The sinusoid test signal is given by $$ s(t) = V_0\cos(2\pi f_0) $$ and its Fourier transform by $$ S(f) = \frac{V_0}{2}\big[\delta(f-f_0) + \delta(f+f_0)\big]. $$ Inserted in $S_\mathrm{AM-DSB-C}$ it ...

View answer
Number of samples in one period of subcarrier after IFFT
5 votes

If you'd like to think analog, an OFDM signal can be written as a sum of weighted complex sinusoidals: $$ x(t)=\sum_{k=0}^{N-1}X_k \exp{\left( \mathrm j 2\pi\frac{kf_\mathrm{s}}{N}t \tag{1}\right)}, $$...

View answer
Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal
5 votes

The frequency resolution $f_\Delta$ is $$ f_\Delta = \frac{f_\mathrm{s}}{N}, $$ where $f_\mathrm{s}$ is the sampling frequency and $N$ is the FFT size. So $$ N = \frac{f_\mathrm{s}}{f_\Delta} = \frac{...

View answer
Alamouti code after or before IFFT block in OFDM
Accepted answer
5 votes

The basic concept of OFDM is to divide a high-bitrate datastream into $N$ low-bitrate datastreams and to multiplex these low-bitrate datastreams in frequency. That is, every datastream is assigned to ...

View answer
Hermitian symmetry in OFDM systems
5 votes

The Hermitian symmetry is used to obtain a real-valued time-domain signal. It is a special case of OFDM called discrete multitone (DMT). It exploits a property of the discrete Fourier transform (DFT), ...

View answer
What can we deduce about variance when we are given the noise spectral density?
Accepted answer
5 votes

Given a low-pass signal $x$ that is a realization of random variable $X$ with constant spectral density $a=N_0/2$ in $f=-B\ldots B$ (and zero otherwise) we can calculate the mean power of that signal ...

View answer
FPS to Hertz in a camera
Accepted answer
5 votes

The physical definition of frequency is the number of oscillations per second and measured in Hertz (Hz) or more general: 1/(duration of one period of a periodic event in seconds). In your case the ...

View answer
What type of correlation is this equation?
Accepted answer
4 votes

I understand your confusion because the equation is barely understandable from the information given in the book. It becomes more clear from the original paper by Classen and Meyr [1] from which it ...

View answer
Reason of Fast Fourier and Inverse Fast Fourier
Accepted answer
4 votes

FFT and IFFT are algorithms that implement the (inverse) discrete Fourier transform (DFT). These transforms convert a signal into another representation, namely the frequency domain, and back. This ...

View answer
Implementing FFT in Matlab
4 votes

For calculating the frequency spectrum of an non-uniformly sampled signal I see two options: Interpolate the data in order to obtain evenly spaced samples before taking the FFT as suggested by Hasan. ...

View answer
Bandwidth of a communication system
Accepted answer
4 votes

In order to avoid inter symbol interference (ISI) the baseband transmit signal must meet Nyquist's first criterion. In frequency domain it can be formulated as follows. $$ \omega_\mathrm{N} = \frac{v_\...

View answer
Power spectral density and SNR for AWGN
Accepted answer
4 votes

First a comment on your noise-generation process. The Matlab function randn() generates Gaussian noise with zero mean and mean power 1. So steps 2 and 3 are obsolete. If you'd like to achieve a given ...

View answer
Is it possible to transmit and/or receive multiple types of signals at the same time?
Accepted answer
4 votes

Theoretically it's possible to do a frequency multiplex of two different protocols with one SDR transmitter. However, the practical main limitation is the speed of the digital-to-analog converter (DAC)...

View answer
Pilot symbols in IEEE 802.11a
Accepted answer
3 votes

A frequency offset $f_\mathrm{off}$ between the carrier frequency and the local oscillator (at the receiver) results in a linear phase, i.e. the received signal contains a factor $\mathrm{exp}(j2\pi ...

View answer
Differential BPSK vs BPSK what are the advantages and disadvantages?
Accepted answer
3 votes

Differential BPSK As the information is encoded in the phase difference of two consecutive symbols, phase estimation can be omitted in systems where the carrier phase can be assumed to be constant ...

View answer
Questions Downlink OFDMA in LTE
Accepted answer
3 votes

In LTE downlink, users are multiplexed in both time and frequency domain. The concept of ressource blocks (RB) describes a certain frequency band in a certain time slot. Your understanding of the ...

View answer
How to implement the imaginary part of FFT equation applied to a signal in computer/C++?
Accepted answer
3 votes

In computer programs, complex numbers are usually represented by an array, field or vector containing two values: one value represents the real part, the other represents the imaginary part of the ...

View answer
OFDM transmitter bandwidth
Accepted answer
3 votes

What should the bandwidth of the BPSK OFDM signal be after resampling? Is it 50 Hz (according to theoretical graph shown), 40 Hz (simulated before resampling) or 80 Hz? What you call resampling ...

View answer