Write the advantages and disadvantages of Numerical interpolation?
Answers
Step-by-step explanation:
Answer :
Smoothing trades horizontal resolution and bandwidth for vertical resolution. It has the benefit of reducing noise above the bandwidth traded off. The disadvantages include requiring a greater record length and/or a higher sample rate to allow for the trade off. Amplitude measurement error can also be a problem.
Sine x/x and linear interpolation are two ways to join the sample points acquired on a waveform. If the signal is a band limited waveform (that is, if there is little frequency content in the waveform above the Nyquist frequency, half the sample rate) then sine x/x interpolation applied with a high quality algorithm can properly and accurately reconstruct the waveform shape and amplitude up to a frequency of 0.4 to 0.25 times the sample rate.
If the waveform is a fast rise pulse, with fast edge features with non-band limited frequency content, then linear interpolation may provide a more faithful representation.
Answer:
Interpolation Methods
Interpolation is the process of using points with known values or sample points to estimate values at other unknown points. It can be used to predict unknown values for any geographic point data, such as elevation, rainfall, chemical concentrations, noise levels, and so on.
The available interpolation methods are listed below.
INVERSE DISTANCE WEIGHTED (IDW)
The Inverse Distance Weighting interpolator assumes that each input point has a local influence that diminishes with distance. It weights the points closer to the processing cell greater than those further away. A specified number of points, or all points within a specified radius can be used to determine the output value of each location. Use of this method assumes the variable being mapped decreases in influence with distance from its sampled location.
IDW Interpolation; Courtesy: QGIS
IDW Interpolation; Courtesy: QGIS
The Inverse Distance Weighting (IDW) algorithm effectively is a moving average interpolator that is usually applied to highly variable data. For certain data types it is possible to return to the collection site and record a new value that is statistically different from the original reading but within the general trend for the area.
The interpolated surface, estimated using a moving average technique, is less than the local maximum value and greater than the local minimum value.
IDW Interpolated Surface
IDW Interpolated Surface; Courtesy:ESRI
IDW interpolation explicitly implements the assumption that things that are close to one another are more alike than those that are farther apart. To predict a value for any unmeasured location, IDW will use the measured values surrounding the prediction location. Those measured values closest to the prediction location will have more influence on the predicted value than those farther away. Thus, IDW assumes that each measured point has a local influence that diminishes with distance. The IDW function should be used when the set of points is dense enough to capture the extent of local surface variation needed for analysis. IDW determines cell values using a linear-weighted combination set of sample points. It weights the points closer to the prediction location greater than those farther away, hence the name inverse distance weighted.
The IDW technique calculates a value for each grid node by examining surrounding data points that lie within a user-defined search radius. Some or all of the data points can be used in the interpolation process. The node value is calculated by averaging the weighted sum of all the points. Data points that lie progressively farther from the node influence the computed value far less than those lying closer to the node.
IDW
A radius is generated around each grid node from which data points are selected to be used in the calculation. Options to control the use of IDW include power, search radius, fixed search radius, variable search radius and barrier.
Note: The optimal power (p) value is determined by minimizing the root mean square prediction error (RMSPE).
ADVANTAGES
Can estimate extreme changes in terrain such as: Cliffs, Fault Lines.
Dense evenly space points are well interpolated (flat areas with cliffs).
Can increase or decrease amount of sample points to influence cell values.
DISADVANTAGES
Cannot estimate above maximum or below minimum values.
Not very good for peaks or mountainous areas.