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To take advantage of another human vision characteristic less sensitivity to complex detail JPEG divides the image into small blocks and applies a discrete cosine transform (DCT) to the blocks, which is a mathematical function that changes spatial intensity values to spatial frequency values This describes the block in terms of how much detail changes, and roughly arranges the values from lowest frequency (represented by large numbers) to highest frequency (represented by small numbers) For areas of smooth colors or low detail (low spatial frequency), the numbers will be large For areas with varying colors and detail (high spatial frequency), most of the values will be close to zero A DCT is an essentially lossless transform, meaning that an inverse DCT function can be performed on the resulting set of values to restore the original values In practice, integer math and approximations are used, causing some loss at the DCT stage Ironically, the numbers are bigger after the DCT transform The solution is to quantize the DCT values so that they become smaller and repetitive Quantizing is a way of reducing information by grouping it into chunks For example, if you had a set of numbers between 1 and 100, you could quantize them by 10 That is, you could divide them by 10 and round to the nearest integer The numbers from 5 to 14 would all become 1s, the numbers from 15 to 24 would become 2s, and so on, with 1 representing 10, 2 representing 20, and so forth Instead of individual numbers such as 8, 11, 12, 20, and 23, you end up with 3 numbers near 10 and 2 numbers near 20 Obviously, quantizing results in a loss of detail Quantizing the DCT values means that the result of the inverse DCT will not exactly reproduce the original intensity values, but the result is close and can be adjusted by varying the quantizing scale to make it finer or coarser More importantly, as the DCT function includes a progressive weighting that puts bigger numbers near the top left corner and smaller numbers near the lower right corner, quantization and a special zigzag ordering result in runs of the same number, especially zero This may sound familiar Sure enough, the next step is to use run-length encoding to reduce the number of values that need to be stored A variation of run-length coding is used, which stores a count of the number of zero values followed by the next nonzero value The resulting numbers are used to look up symbols from a table The symbol table was developed using Huffman coding to create shorter symbols for the most commonly appearing numbers This is called variable-length coding (VLC) See Figures 26 and 28 for examples of DCT, quantization, and VLC The result of these transformation and manipulation steps is that the information that is thrown away is least perceptible Since the eye is less sensitive to color than to brightness, transforming RGB values to luminance and chrominance values means that more chrominance data can be selectively thrown away And since the eye is less sensitive to high-frequency color or brightness changes, the DCT and quantization process removes mostly the high-frequency information JPEG compression can reduce picture data to about one-fifth the original size with almost no discernible difference and to about one-tenth the original size with only slight degradation.

The formula returns 3, the number of times numbers appear in the range B2 : C4 COUNTA Unlike COUNT, COUNTA counts both numbers and text In the illustration above, COUNTA(B2 : C4) would return the number 6 COUNTIF This is a combination conditional and counting function It is similar to the SUMIF but returns a count of the items that meet the condition, rather than the sum It only has two arguments The syntax is: = COUNTIF Range,Criteria Range is a list of items Criteria is a condition related to Range The following shows the number of items related to the category Alex

simulatedService.AssertWasCalled( svc => svc.LogError("name too short:abc.ext")); } //the same test using Typemock Isolator AAA syntax [Test] public void CreateMock_Isolator() { IWebService simulatedService = Isolate.Fake.Instance<IWebService>(); LogAnalyzer log = new LogAnalyzer(simulatedService); log.Analyze("abc.ext");

2-18

2-19

= =COUNTIF(B2:B7,E2)

Isolate.Verify.WasCalledWithExactArguments(()=> simulatedService .LogError("name too short:abs.ext")); }

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If you want to count the number of items that are equal (or above or below) a certain value, you can also use COUNTIF In this case, the Criteria must be stated as a test The following example shows the number of items that are above 25 and looks to the range C2:C7

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