Signal ProcessingoverviewSignal processingSignal processing GoalsSignal processing needsSignal processing todayWhat is a signal?Time Domain and Frequency DomainThe time domainThe frequency domainConverting analog to digital signalsSignal samplingSlide 13Types of Signals.Types of signalsSlide 161-d signals2-d signals.3-d signals.Why do we want to process a Signal?Why do we want to process A signal?Techniques for processing a signalDiscrete Fourier transformDiscrete Fourier transformDiscrete f0urier transformFast Fourier transformFAST Fourier transformProperties of FFT2-d ConvolutionMore 2-d convolutionImage Processing IN Computer VisionImage processing IN computer visionquestionsreferencesThomas Dohaney COT 4810Signal Processing Goals, Needs, Applications.What is a signal?Types of signals.Reasons to process signals.Analog to Digital conversion.Digital Filters.Time domain and frequency domain.Discrete Fourier Transforms and Fast Fourier Transforms and their properties.Image processing and Computer Vision.An area in Computer Science that is unique by the type of data it uses, signals.Signals are sensory data from physical systems .Vibrations Visual images Voltage SoundSignal Processing is MathematicsAlgorithmsTechniquesTo manipulate signalsLots of goalsEnhancement of visual imagesRecognition and generation of speechCompression of data for storage and transmissionObject detectionImage enhancement1960s and 1970s Digital computers first became availableComputers were expensiveSP was limited to only a few critical applications. Pioneering efforts were made in four key areas.RADAR and SONAROil ExplorationSpace ExplorationMedical ImagingToday SP driven by Commercial marketplaceNeed to transfer informationA signal is a function that conveys information, generally about the state or behavior of a physical system.Analog signals are continuous time, continuous amplitude.Digital signals are discrete time, discrete amplitude.Many ways that information can be contained in a signal. Manmade signals. AMFMSingle-sideband Pulse-code modulation Pulse-width modulationOnly two ways that are common for information to be represented. Information represented in the time domain, Information represented in the frequency domain.Domain describes when something occursWhat the amplitude of the occurrence was Each sample in the signal indicates What is happening at that instant, and the Level of the event If something occurs at time t, the signal directly provides information on the time it occurred, the duration, and the development over time. Contains information that is interpreted without reference to any other part of the sample.Frequency domain is considered indirect.Information is contained in the overall relationship between many points in the signal.By measuring the frequency, phase, and amplitude, information can be obtained about the system producing the motion.Converting continuous time, continuous amplitude To discrete time, discrete amplitudeTo convert to a digital signal we must sample it at a rate, so there is enough information to reconstruct it, and not leave any information out.Why we convert the signal to digital form.Software implementationsAccuracy can be controlledRepeatableNoise is minimalOperations are easier to implement Digital storage is cheapSecurityPrice and performanceTrade offs.Loss of informationAD and DA conversion requires additional hardwareSpeed of processors is limitedRound off errorsNyquist sampling theorem. The lower bound of the rate at which we should sample a signal, in order to be guaranteed there is enough information to reconstruct the original signal is 2 times the maximum frequency.Now in its digital form,we can process the signalin some way..1-D signals. Sound and Vibrations. Signals used to extract statistical characteristics, and construct a mathematical model of the signal.Output signal is entered into the mathematical model, if only white noise is observed it is normal, it is abnormal if there is a lack of white noise. Typically used to diagnose a system in that they are used to detect abnormality and deterioration.2-D signals.Considered to be an image signal.Signal is distorted in the digitizing process based on signal to noise ratio. (blur, movement, arithmetic, or color distortion).Typically to determine measurement of an object in an image, image restoration, visualization to extract physical information, pattern recognition, image inspection and fault detection.3-D signals.Computer vision.Signal is obtained by visual sensor composed of many two dimensional images, or by measuring distance of an object (using electromagnetic wave, or laser) and adding this information to an object in a 2-d signal.Typically used in automation, remote sensing.Seismic vibrationsEEG and EKGSpeechSonarAudio Musicph - o - n - e - t - i - c - ia - nPhotographsMedical imagesRadarIED detectionSatellite dataFaxFingerprintsy (cm)x (cm) ISAR (x,y)-60 -40 -20 0 20 40 60-60-40-200204060Video Sequences Motion SensingVolumetric data sets Computed Tomography, Synthetic Aperture Radar Reconstruction)Compare a transmitted and reflected signal Find characteristics of a remote objectRecognize what’s in a signalTarget detectionSpeech recognitionImage analysis Predict a future value of the signalStock market prediction Interpolate missing values of a signalConceal lost video packetsRestore a signal that has been degradedNoise removalEcho cancellationObtain a visual representation of a signalExtract informationEnhance a signalImage contrast enhancementCompress a signalFaster transmissionLess storage space Synthesize a realistic example of a signalSpeech generation and synthesisImage texture generationChoose specific input signals to control a processFace detectionMotion detectionA system is a function that produces an output signal in response to an input signal.An input signal can be broken down into a set of components, called an impulses.Impulses are passed through a system resulting in output components, which are synthesized
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