PowerShell copy files with filter and maintain directory structure

Copy-FilesRecurseWithFilter.ps1

$sourceDir = 'C:\SourceDir\'
$targetDir = 'C:\DestDir\'

Get-ChildItem $sourceDir -Filter "*" -Recurse |` 
  Where-Object {$_.LastWriteTime -gt (Get-Date).addDays(-1) -and -not $_.PSIsContainer} |`
  foreach {
    $targetFile = $targetDir + $_.FullName.SubString($sourceDir.Length);
    New-Item -ItemType File -Path $targetFile -Force;
    Copy-Item $_.FullName -destination $targetFile
  }