What is the difference between DTFT and DFT?

The difference between DTFT and DFT is that it is substantively different.

Discrete Fourier transformThe essence of DFT: the discrete-time Fourier transform.

2. The essence of the discrete-time Fourier transform DTFT: the Fourier transform of the sequence.

The results are different for both:

Discrete Fu, for a general periodic signal, can be used as a series of (finite or infinite) sine waves.

superposition of the representation. There are several such types: DTFT (Time Discrete, Frequency Continuous) DFT (Time and Frequency are discrete, available on a computer.

DFT is a sample of DTFT, so the value of DFT is the same as the value of DTFT, and the same is true for the imaginary part. DTFT is the discrete-time Fourier transform.

That is, the z-transformation on the unit circle.

It can be said that the Fourier transform is a special case of the z-transform.

Discrete-time Fourier transforms are sometimes referred to as sequential Fourier transforms. The discrete-time Fourier transform is essentially a single discrete-time Fourier transform (DTFT) that allows us to transform our products in the frequency domain.

DFT is a discrete form of the Fourier transform, which is the function x[(introduced into the Laplace transform) obtained by discrete sampling of x(t) after the Fourier transform.

Explain that the z-transform below is one of the discrete-time Fourier transform (DTFT).

DTFT is a finite-length discrete signal real spectrum, and DFT is a false spectrum sampled at equal intervals from 0 to 2, DFT can only estimate some information of the DTFT spectrum, but in fact it does not exist, in addition, DFT is also a DFS de-principal value sequence.

In short, you should remember that DFT can only be used as an estimate of the real spectrum DTFT and DFS, so that we know the distribution of the spectral density of discrete sequences.

DFT stands for Discrete Fourier Transform.

The Discrete Fourier Transform (DFT) is a Fourier transform that transforms the time-domain sampling of a signal into the frequency-domain sampling of its DTFT in both the time and frequency domains. Formally, the sequence of transformations at both ends (kib in the time and frequency domains) is finitely long, and in fact both sets of sequences should be considered as the principal value sequence of the discrete periodic signal. Even if DFT is used for a discrete signal of finite length, it should be considered as a transformation of its periodic extension.

In practical applications, fast Fourier transform is usually used to calculate DFT.

In short, although the addition of these structures in the design stage increases the complexity of the circuit and seems to increase the cost, it can often save more time and money in the testing stage.

dftdensity functional theory.

Dftdry Film Thickness refers to the thickness of the coating after the paint film has dried.

dtft is to discretize the original signal in the time domain, while dft is to detft inFrequency domainDiscretization.

This is equivalent to the DFT discretizing the original signal in both the time and frequency domains, and for DFT, it is a Fourier of a finite-length signal.

representation, while DTFT is a Fourier representation of an infinitely long signal.

Features of DTFT and DFT:

1. The nature is different.

The frequencies in the DTFT transformed graph are generally continuous (except for special functions such as COS(WN), which are transformed into shock strings), while DFT is an equally spaced sampling of DTFT, which is discrete points.

2. Different uses.

DFT is entirely computer technology.

Because if you don't have a computer, you can use a DTFT analysis to see the frequency response.

3. The characteristics are different.

DTFT transforms the discrete-time signal x(n) into a continuous frequency domain, the spectrum is periodic, and the period is 2, and the original signal is an absolute number if it is a non-periodic function.

The dtft is transformed as a continuous function.

If the original signal is a periodic function and the dtft is a discrete function.

In terms of form, the sequence at both ends of the transformation (time domain and frequency domain) is finitely long, but in fact both sets of sequences should be regarded as the principal value sequence of the discrete periodic signal, and even if the finite-length discrete signal is DFT, it should be regarded as the transformation of its periodic extension.

dft（Discrete Fourier transform) is generally referred to as a discrete Fourier transform.

The Discrete Fourier Transform (DFT) Fourier Transform (DFT) Fourier analysis method is the most basic method of signal analysis, and the Fourier transform is the core of Fourier analysis, through which the signal is transformed from the time domain to the frequency domain, and then the spectral structure and change law of the Huai answer signal are studied.

Physical significanceLet x(n) be a finitely long sequence of lead filial piety n, then its Fourier transform and z transform.

and the discrete Fourier transform are expressed by the following three relations:

x(e^jω)=n=x(n) e^j-ωn。

x(z)= n=x(n)z^-n。

x(k)= n=x(n) e^-j2πkn/n。

The z-transform on the unit circle is the Fourier transform of the sequence.

The discrete Fourier transform is the equally spaced sampling of the spectrum x(ej) of x(n) at n points on [0,2], that is, the discretization of the sequence spectrum, which is the physical meaning of DFT.

DTFT is a representation of CTFT after sampling (discretization) in the time domainFrequency domainOn or continuous. DFT is a representation of DTFT sampled (discretized) on frequency. As a result, DFTs are discrete in both the frequency and time domains, allowing them to be processed using computers.

In fact, it can also be accessed from DTFS (Discrete Time Fourier Series Toucher.

to understand DFT. Consider a discrete-time signal, cut it off, and then extend it periodically according to the truncated signal. This is to construct a discrete intermantial periodic signal with a single period of the interception signal.

For a periodic signal, we can find its discrete Fourier series, and the coefficients of these Fourier series are the coefficients of DFT in the frequency domain.

As you can also see from the name, DTFT is a discrete-time Fourier transform.

It's just temporally discretized; DFT is a discrete Fourier transform that is discrete in both the time and frequency domains.

The full name of DTFT

"DTFT" is an abbreviation for "Discrete Time Fourier Transformation", and the Chinese term is "Discrete Time Fourier Transformation".

The traditional Fourier transform (FT) can only be used to analyze the spectrum of continuous-time signals, while computers can only process discrete digitally coded messages, so modern society needs to perform Fourier analysis on a large number of discrete time series signals. DTFT is one of the mathematical tools used in the IT field for spectral analysis of discrete-time signals.

The problem with the Fourier transform is that it contains too much infinity to actually use, and there are three inherent infinities.

Infinite Integral – Signals are integrated over time.

Continuous Frequency – A signal is made up of an infinite number of adjacent frequencies.

Continuous Time Signal – The signal contains a value at each moment, i.e., an infinite number of hour wheel ticks.

Transform formulas. The discrete-time Fourier transform does not get rid of infinity 1 and 2, but it does eliminate infinity 3. Let's compare the male tremor block formula comparing the Fourier transform and the discrete-time Fourier transform.

In fact, DTFT is a special kind of z-transform. In the z-transform, if the complex variable z is only in the unit circle of the z-plane (r=|z|=1 or =0), the complex variable is converted into a pure virtual variable.

Limitations of DTFT:

The Discrete-Time Fourier Transform (DTFT) is a special Z-transform, which has important theoretical significance in mathematics and signal analysis. However, it is more difficult to do computing with a computer.

This is because, in the DTFT transformation pair, the discrete time series is discrete at time n, but its spectrum is a continuous periodic function at the digital angular frequency. Whereas, computers can only process digital signals that are discrete by variables.

distance to the point of failure; dielectric films; fault point location; fault location; Distance to failure. It is a tool for antenna transmission line service maintenance, line performance verification, and fault analysis. Frequency Domain Reflectance (FDR) measurement techniques are used in DTF.

FDR is a transmission line fault isolation method that accurately identifies signal path attenuation over coaxial cables and waveguide transmission lines.

For example, the use of DTF can detect the best damage of the cable, the cable in the manufacturing process due to the cable length, cable type, material differences or other factors may cause some parts of the cable to have pits or cracks, and these problems are difficult to observe and inspect by eye, but the use of DTF can quickly detect the defects of the cable.

dtf macro instruction Defines the macro instructions of the file.

Low Aldehyde Finishing Agent DTF 7 for Textile Textile Less aldehyde Finishing Agent DTF-7

Detong DTF light multi-wing centrifugal fan. Detong DTF light multi-wing centrifugal fan is a kind of multi-wing centrifugal fan independently developed by Guangdong Zhaoqing Detong, which is a kind of multi-wing centrifugal fan with high static pressure, low noise and small size specially developed for purification, environmental protection industry and various special equipment.

How it works:Detong DTF light multi-wing centrifugal fan is a machine that relies on the input mechanical energy to increase the gas pressure and discharge the gas, it is a driven fluid machine. According to the principle of converting kinetic energy into potential energy, a high-speed rotating impeller is used to accelerate the gas, then decelerate and change the flow direction to convert kinetic energy into potential energy (pressure).

In a single-stage centrifugal fan, the gas enters the impeller from the axial direction, changes to a light direction as it flows through the impeller, and then enters the diffuser. In a diffuser, the gas changes the direction of flow causing a deceleration, which converts kinetic energy into pressure energy. The increase in pressure occurs mainly in the impeller and to a lesser extent in the expansion process.

In a multistage centrifugal fan, a reflux is used to bring the air to the next impeller, creating a higher pressure.

The above content reference: Encyclopedia-Detong DTF light multi-wing centrifugal fan.