分析講稿ni培訓labview rf

1、Lesson 2 Fourier Transform and FFTsFrequency versus Time DomainFourier TransformRelationship of Time and FrequencyNyquist SamplingCoherent Sampling and WindowingSignal to Noise Ratio (SNR)IQ plex FFTTimeAmplitude(power)FrequencyTime DomainMeasurementsFrequency DomainMeasurementsA. Frequency vs. Time

2、 DomainFrequency DomainTime DomainAnalyzing Performance Using the Frequency DomainB. Fourier TransformInverse Fourier TransformTranslates signals back and forth between time domain and frequency domainNot very useful for digitized signalsUse discrete Fourier transform (DFT)Discrete Fourier Transform

3、 (DFT)DFT is a N2 mathematical operation.IDFT is the inverse of DFT.FFT is an N ln (N) mathematical operation.FFT provides an equivalent result with much fewer calculations.Zoom FFT AlgorithmsC. Relationship of Time and FrequencyWider in time = narrower in frequencyNarrower in time = wider in freque

4、ncyCommon TransformationsftfttTs-TsfDC TransformationImpulse Train TransformationImpulse TransformationD. Nyquist SamplingReconstruction guaranteed if Fs 2 FmaxEach copy centered around integer multiples of FsAliasingDownconverted signal could have “other” frequency content. 100 MHz digitizer would

5、simply allow under sampling (not desired).Utilize LPF before digitizer to band-limit the signal and assure no aliasing. Exercise 2-1: Lowpass SamplingDetermine the Nyquist sampling rate for real lowpass signal and examine the aliasing effect.Exercise 2-2: Band Pass SamplingStudy under sampling techn

6、ique and determine set of sampling rates that are less than fmax.Time vs. FrequencyUse the FFT to observe a sinusoidal signal with added noise in both the time domain and frequency domain.Getting Started Real SignalObserve that the FFT of real signals is symmetric about the N/2 bin (that is, only ha

7、lf the bins are meaningful).E. Coherent Sampling and WindowingEach bin of FFT represents specific frequency.If a time domain signal is sampled improperly (noncoherently), leakage across bins occurs.To prevent leakage, sample coherently according to the following relationship: whereFs = Digitizer sam

8、pling frequency N = Number of samples (usually a power of 2)Ft = Frequency of signal we are measuring M = Number of cycles of the signal we captureWindowingNever use windowing if coherency guaranteed. Disadvantages:Widens the frequency spectrum (smearing)Raises noise floorAdvantage: De-emphasizes di

9、scontinuities Windowing Noncoherent SignalsNo Window 5 cycles captured (180 phase shift) Peak of FFT is in bin 5 Very poor SNRHamming WindowDe-emphasizes edgesPeak still at bin 5SNR improvedWindowing Noncoherent Signals (Continued)No Window:Same as previous Blackman Window:More de-emphasis around ed

10、ges, peak still at bin 5, SNR more improvedHowever, signed has more “smearing” (that is, a broader spike)Comparison of WindowsF. Signal-to-Noise Ratio (SNR)To determine SNR compare peak signal to noise floor.SNR does not include harmonics, or other spurious tones.Example: Real-World Signal (Coherent

11、ly Sampled)Cosine + two harmonics + DC + noise + spursAcquired 200 cyclesNotice that in the time domain it is difficult to discern other components, but in frequency domain, these components are highlighted.Example: Real-World Signal (Noncoherently Sampled)No WindowingNearly all information is lostH

12、anning Windowed FFTMost information discernable; tones are, however, smearedCoherency vs. non-CoherencyObserve leakage caused by improperly sampling (noninteger cycles) of a sinusoid.Frequency Responses of Various Windows (optional)Observe leakage caused by improperly sampling (noninteger cycles) a

13、sinusoid.Effects of Windowing (optional)Observe leakage caused by improperly sampling (noninteger cycles) a sinusoid.G. IQ Modulation / Complex FFTReal SignalsPositive and negative frequency identical; mirror imageOnly concerned with N/2 points of an FFTComplex SignalsPositive and negative signals a

14、re not identical.Must examine all N points of an FFT I = In-phase = Real Signal Q = Quadrature = Imaginary SignalI and Q must be orthogonal to one another (90 separated)Amplitude/Phase Imbalance with Complex FFTQ (solid line) leads I (dashed line) by 90200 cycles captured using 2,048 pointsNo signal

15、 at bin 200Bin 1848 (2048 200) contains peakSignal in negative frequency because Q leads IAmplitude/Phase Imbalance with Complex FFT (Continued)0.0001 % amplitude imbalance added to signal1 Vp signal indicates less than 1 mV of amplitude imbalance2 peaks now seen ( M = 1848 and M = 200)M = 200 at 50

16、 dBc represents amplitude imbalancePhase Imbalance Using Complex FFTSignals phase imbalanced by 0.2 degreesM = 200 shows 56 dBcEnsuring bin M = 200 56 dBc to ensures amplitude and phase specificationComplex FFTsExamine the non-symmetrical behavior of complex signals.Amplitude ImbalanceExamine what h

17、appens when we introduce an amplitude imbalance between the sine and cosine signals.Phase ImbalanceExamine what happens when we introduce phase imbalance between the sine and cosine signals.Complex Signal PropagationExamine the orthogonal nature of cosine and sine.SummaryViewing data in the frequency domain shows different information than viewing data in the time domain.We capture these voltage time domain signals and then analyze their fr