Common formula:
x (n) is the z-transform
x (n) of the discrete-time Fourier transform is positive
Discrete Fourier transform for the series
Four forms Fourier transform 3.1
3.1.1. Continuous time Fourier transform function
Time is continuous, non-periodic: ■ The Fourier transform of a continuous function of time / Fourier Transform (CFT / FT)
It is continuous in time, period: ■ The Fourier series (CFS) is a continuous periodic signal
Continuous time period of signal may be characterized by a linear combination of a series of harmonic components.
Expansion: 
there will be summed up later, do not be afraid not tell
3.1.2 continuous time series the Fourier transform
■ discrete-time Fourier transform (the DTFT)
■ discrete Fourier series (DFS)
DTFT finite sequence of frequency-domain samples, the sequence will be a time domain extension cycle; spectrum corresponding to the periodic sequence is a discrete period and may be characterized by a linear combination of a periodic sequence of a series of harmonic components;
3.1.3. Fourier transform, the relationship between the frequency domain
■ When the Fourier transform, the relationship between the frequency domain
Fourier transform means a transformation between the time signal and the frequency spectrum function.
| name | Time Functions |
Frequency function |
| Fourier transform (FT / CFT) |
Continuous time aperiodic | Non-periodic, continuous spectrum |
| Fourier series continuous periodic signal (CFS) | Continuous time period |
Aperiodic, discrete spectrum |
| Continuous time series the Fourier transform (the DTFT) | Discrete-time aperiodic |
Cycle, continuous spectrum |
| Periodic sequence of discrete Fourier series (DFS) |
Discrete time period | Cycle, discrete spectrum |
Memorize:
| non- | even |
| week | from |
Even non-consecutive weeks from the time domain + -> aperiodic frequency domain; discrete time domain -> cycle frequency domain
3.2 Fourier transform DFS periodic sequence
Because N is the continuation of the cycle, doing so as long as the number of stages in a cycle of transformation on it
3.2.1. Discrete Fourier series DFS
■ discrete Fourier series (the DFS) --- defined formula
■ discrete Fourier series (DFS) - define the rotation factor
Positive Negative
■ discrete Fourier series (DFS) - Nature twiddle factor
Function words are derived
① Inside negation, conjugation, and just outside the offset
② about sex can help FFT, W above i can move down
③ periodic rotation factor
⑤e of jΠ = 1, e is -jΠ = -1
3.2.2. The relationship between transitions
■ relationship with DFS z-transform, DTFT of
②DFS DTFT made of a N-point sampling in a period 2Π
③Z do transform transform on the unit circle, is the DTFT
DTFT在做一个等间隔采样，得到DFS
——>在单位圆做一个等间隔采样就能得到DFS
做一个周期序列N=8的例子
在单位圆做一个8点的等间隔采样就能得到DFSx~
等比数列求和公式：，
sinx=[e^(ix)-e^(-ix)]/(2i)，cosx=[e^(ix)+e^(-ix)]/2 ，又用到了欧拉公式
3.2.3.DFS的性质
DFS是周期离散序列的傅立叶变换，因此DFS具有一些可以类比CFT的性质。
■DFS 的性质--线性性质
注意必须要周期相等，才能线性组合
■DFS 的性质--移位性质
注意符号的正负
后面不写了，来不及复习了，刷原题去